REPORT SERIES IN AEROSOL SCIENCE
N:o 144 (2013)
STUDIES ON THE CONNECTIONS BETWEEN ATMOSPHERIC
SULPHURIC ACID, NEW PARTICLE FORMATION
AND CLOUD CONDENSATION NUCLEI
Division of Atmospheric Sciences
Department of Physics
Faculty of Science
University of Helsinki
To be presented, with the permission of the Faculty of Science
of the University of Helsinki, for public criticism in auditorium E204,
Gustaf Hällströmin katu 2, on November 29 th , 2013, at 12 o’clock noon.
Author’s address: Sanna-Liisa Sihto-Nissilä
Department of Physics
P.O. Box 64
FI-00014 University of Helsinki
Professor, Ph.D. Markku Kulmala
Division of Atmospheric Sciences
Department of Physics
University of Helsinki
Ph.D., docent Michael Boy
Division of Atmospheric Sciences
Department of Physics
University of Helsinki
Professor, Dr. Tech. Kari Lehtinen
Department of Physics, University of Eastern Finland, and
Finnish Meteorological Institute, Kuopio Unit
Ph.D., docent Harri Kokkola
Finnish Meteorological Institute, Kuopio Unit
Professor, Ph.D. Aijun Ding
School of Atmospheric Sciences
Nanjing University, China
Professor, Ph.D. Erik Swietlicki
Division of Nuclear Physics
Department of Physics
Lund University, Sweden
ISBN 978-952-5822-78-6 (printed version)
ISBN 978-952-5822-79-3 (electronic version)
Helsingin yliopiston verkkojulkaisut
This thesis was made during 2004–2013 at the Division of Atmospheric Sciences of
University of Helsinki. I express my gratitude to Prof. Markku Kulmala, head of the
division, for the opportunity to work with such an interesting subject, atmospheric
science, in a motivated group. I thank the head of the Department of Physics, Prof.
Juhani Keinonen, for providing the working facilities needed for the research.
While located in the Department of Physics, the research at the Division of Atmospheric
Sciences is a fascinating multidisciplinary combination of physics, chemistry,
meteorology and even biology. I am grateful to have been able to work in this interesting
field, which in some aspects still resembles how natural sciences once started:
let’s go out to nature and see how it works! In our division people have mainly gone to
the forest in Hyytiälä and measured how new particles are formed there. During these
years, I have learned many interesting things — and many of them outside the basic
physics — for example which gases trees are emitting when they are stressed and how
water is transported in a tree.
I thank all my coauthors for good research co-operation. Especially I want to thank
Ilona Riipinen for excellent co-operation in preparing paper II, Hannele Korhonen for
giving her UHMA-code to my use, Henri Vuollekoski and Johannes Leppä for doing
modelling work together, and Joonas Vanhanen and Jyri Mikkilä for co-operation in
my last paper about CCN. This thesis combines modelling and analysis of field data. I
personally did not participate the measurements, and therefore I want to acknowledge
all researchers responsible for measurements as well as the technicians working at the
field stations for providing the data used in this thesis.
I thank my supervisors Kari Lehtinen and Michael Boy for guidance during the
whole path of PhD studies. Veli-Matti Kerminen deserves thanks for commenting
the manuscripts and for supervision when I was finalizing this thesis. I thank my reviewers
for the constructive comments to improve the introduction part as well as PhD
Theo Kurtén for proofreading the thesis. Maj and Tor Nessling Foundation (project no
2008310) and Academy of Finland (Center of Excellence Program) are acknowledged
for financial support.
I thank all the staff at the Division of Atmospheric Sciences for creating a nice working
environment andofferinggoodcompany. Beingnostalgic, Iwant tomentionthe”gang”
who started the doctoral studies at about the same time and/or with whom I shared
a room: Ilona Riipinen, Anne Hirsikko, Lauri Laakso, Tareq Hussein, Theo Kurtén,
Antti Lauri, Henri Vuollekoski, Tuomo Nieminen, Martta Toivola (Salonen), Johanna
Lauros and Eija Asmi (Vartiainen). Thank you for company in research, studies,
Hyytiälä courses and during conference trips, and for many many discussions both
about scientific and non-scientific topics.
This period of PhD studies coincided with a difficult period in my personal life, and
that certainly has affected my work too and made the period of PhD studies longer
thanexpected. Ithankmy supervisors andcoauthorsforpatience andhumane attitude
— we all are simply humans and face problems from time to time.
I express my gratitude for collaboration and friendship with PhD Amar Hamed, a
colleague from Kuopio, who passed away just two months ago. Thank you Amar for
Last I want to thank my family and relatives for support, especially during the difficult
times. Encouragements personally and via internet were important for finalizing
the thesis this spring/summer. I also have to give my acknowledments to music and
handcrafts, those are often needed to keep things in balance! I am most grateful to my
husband Jaani for support, patience, belief in my abilities even on bad days, and for
all kinds of practical help — this, I guess, may be called love.
In Kumpula, Helsinki, October 2013
ong>Studiesong> on the connections between atmospheric sulphuric acid, new particle
formation and cloud condensation nuclei
Sanna-Liisa Katariina Sihto-Nissilä
University of Helsinki, 2013
Atmosphericaerosol particles (small nmto µmsizedparticles floatingin air) areanimportant
part of the atmosphere and the climate system. Aerosols directly scatter sunlight and influence
cloud formation, thereby causing a net cooling effect on the climate which counteracts
global warming caused by greenhouse gases. Aerosols, particularly those from anthropogenic
pollution, also deteriorate human health.
Aerosols originate either from direct particle emissions or are formed in the atmosphere
from gas-phase vapours through nucleation. Aerosols have both anthropogenic and natural
sources. In the atmosphere, particle formation occurs frequently in continental areas all
around the globe, and it is an important source of aerosol particles and cloud condensation
nuclei. Sulphuric acid is one of the main compounds in atmospheric particle formation, and
it participates both in nucleation and particle growth.
This thesis studied the process of atmospheric particle formation and specifically its connection
to gaseous sulphuric acid, based on analysis of field measurement data and modelling.
New particle formation rates were observed to correlate with sulphuric acid concentration to
the power between 1–2. This correlation was notably different than expected on the basis of
nucleation theories. Based ontheobserved linear andsquaredcorrelation, newsemi-empirical
parameterisations for atmospheric nucleation rate were proposed: the activation and kinetic
nucleation mechanism. Empirical nucleation coefficients were determined from atmosperic
field data measured at two field stations in Hyytiälä, Finland, and Heidelberg, Germany.
The correlation of new particle formation with sulphuric acid and the factors affecting the
correlation were further investigated by performing simulations with an aerosol dynamical
Atmospheric relative humidity was observed to correlate negatively with sulphuric acid concentration
and particle formation rate. It was proposed that cloudiness at high relative humidities
could decrease the amount of UV-radiation reaching the ground, thereby decreasing
the formation of sulphuric acid through a photochemical reaction pathway.
Thisthesis also investigated the ability of aerosol particles in boreal forest to act as cloud condensation
nuclei (CCN). New particle formation events were observed to produce significant
amounts of potential CCN.
The results of this thesis provided new insights on atmospheric particle formation and its
connection to sulphuric acid. The developed nucleation rate parameterisations are useful for
modelling of aerosol formation in regional and global climate models. The CCN parameters
determined for boreal forest environment can be applied in climate modelling to predict
boreal forest aerosols’ effects on climate.
Keywords: atmospheric aerosol, particle formation, nucleation, sulphuric acid, cloud condensation
List of publications 7
1 Introduction 8
2 Atmospheric particle formation 13
2.1 Aerosol size distribution and its dynamics . . . . . . . . . . . . . . . . 15
2.1.1 Condensation and coagulation . . . . . . . . . . . . . . . . . . . 17
2.1.2 General dynamical equation . . . . . . . . . . . . . . . . . . . . 20
2.1.3 Condensation and Coagulation sinks . . . . . . . . . . . . . . . 21
2.2 Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.1 Basic concepts of nucleation theory . . . . . . . . . . . . . . . . 23
2.2.2 Atmospheric nucleation mechanisms . . . . . . . . . . . . . . . . 26
2.2.3 Laboratory measurements of atmospheric nucleation . . . . . . . 28
2.3 Formation and loss processes of sulphuric acid in the
atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4 Activation of aerosol particles to cloud droplets . . . . . . . . . . . . . 34
3 Methods 37
3.1 Experimental data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.2 The calculation of particle formation rate . . . . . . . . . . . . . . . . . 41
3.2.1 Particle formation rate at 3 nm . . . . . . . . . . . . . . . . . . 42
3.2.2 Estimation of the nucleation rate from the apparent particle formation
rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.3 Evaluation of the calculation method of J 3 . . . . . . . . . . . . . . . . 47
3.4 University of Helsinki Multicomponent Aerosol model . . . . . . . . . . 50
4 Connection between sulphuric acid and new particle formation 53
4.1 General correlation of sulphuric acid and new particle formation in the
field data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Activation and kinetic nucleation mechanisms . . . . . . . . . . . . . . 56
4.3 The effect of relative humidity on the nucleation rate . . . . . . . . . . 61
4.4 Modelling the connection between sulphuric acid and particle formation 65
5 CCN activity of boreal forest aerosols 69
5.1 Seasonal variation of CCN properties at the Hyytiälä
SMEAR II station . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 Effect of new particle formation on cloud condensation nuclei . . . . . . 72
6 Review of papers and the author’s contribution 75
7 Summary and conclusions 76
List of publications
This thesis consists of an introductory review, followed by six research articles. In the
introductory part, the papers are cited according to their roman numerals.
I Sihto, S.-L., Kulmala, M., Kerminen, V.-M., Dal Maso, M., Petäjä, T., Riipinen,
I., Korhonen, H., Arnold, F., Janson, R., Boy, M., Laaksonen, A. and Lehtinen,
K. E. J.: Atmospheric sulphuric acid and aerosol formation: implications
from atmospheric measurements for nucleation and early growth mechanisms,
Atmos. Chem. Phys., 6, 4079–4091, 2006.
II Riipinen, I., Sihto, S.-L., Kulmala, M., Arnold, F., Dal Maso, M., Birmili, W.,
Saarnio,K., Teinilä, K., Kerminen, V.-M., Laaksonen, A., Lehtinen, K.E.J.: Connections
between atmospheric sulphuric acid and new particle formation during
QUEST III–IV campaigns in Heidelberg and Hyytiälä, Atmos. Chem. Phys., 7,
III Hamed, A., Korhonen, H., Sihto, S.-L., Joutsensaari, J., Järvinen, H., Petäjä,
T., Arnold, F., Nieminen, T., Kulmala, M., Smith, J.N., Lehtinen, K.E.J., and
Laaksonen, A.: The role of relative humidity in continental new particle formation,
J. Geophys. Res., 116, D03202, 2011.
IV Sihto, S.-L., Vuollekoski, H., Leppä, J., Riipinen, I., Kerminen, V.-M., Korhonen,
H., Lehtinen, K. E. J., Boy, M., and Kulmala, M.: Aerosol dynamics
simulations on the connection of sulphuric acid and new particle formation, Atmos.
Chem. Phys., 9, 2933–2947, 2009.
V Vuollekoski, H., Sihto, S.-L., Kerminen, V.-M., Kulmala, M., and Lehtinen, K.
E. J.: A numerical comparison of different methods for determining the particle
formation rate, Atmos. Chem. Phys., 12, 2289–2295, 2012.
VI Sihto, S.-L., Mikkilä, J., Vanhanen, J., Ehn, M., Liao, L., Lehtipalo, K., Aalto,
P.P., Duplissy, J., Petäjä, T., Kerminen, V.-M., Boy, M., and Kulmala, M.:
Seasonal variation of CCN concentrations and aerosol activation properties in
boreal forest, Atmos. Chem. Phys., 11, 13269–13285, 2011.
Papers I–II and IV-VI are reprinted under the Creative Commons Licence. Paper III
is reprinted with the permission of the journal.
The air surrounding us is a mixture of gases (nitrogen, oxygen, argon, water vapour,
carbon dioxide etc.) and small particles. Air is an example of an aerosol: a mixture of
gas and small particles floating in it. The floating particles are called aerosol particles.
Due to their small size, in most cases aerosol particles are invisible to the human
eye. However, at sufficiently big particle sizes and number concentrations the particles
as smog in polluted cities, dust storms in desert areas or haze in a moist forest. In
additiontotheatmosphere, aerosolsareencounteredinmanytechnicalapplications, for
example: in deodorant spray, paints and other liquids that can be dispersed smoothly
by first spraying them as aerosols to air or in inhalators used in drug delivery. This
thesis deals with aerosol particles in the atmosphere, i.e. atmospheric aerosols.
Atmospheric aerosols originate either from direct particle emissions (primary aerosols)
or are formed in the atmosphere from gases through nucleation (secondary aerosols).
The direct particle emissions include soot and other particle emissions from wood and
fossil fuel combustion, road dust particles, sea salt aerosols suspended to air from
whitecaps on the sea surface, pollen emitted from flowering plants and trees, bacteria
and viruses floating in air, and dust particles removed from Earth’s surface by blowing
wind (e.g. Reid et al., 2005; Engelstaedter et al., 2006; Viana et al., 2008; Hultin et al.,
2011; Wang et al., 2013). These processes generate aerosol particles at all particle
sizes from ∼10 nm upto several tens of µm. In atmospheric particle formation, new
particles areproduced when vapour molecules collide together andformastable cluster
of 1–2 nm size (Kulmala, 2003; Kulmala et al., 2007, 2013). This process is called
nucleation. In the atmosphere, sulphuric acid is considered as the most important
After being emitted to or formed in the atmosphere, aerosol particles are subject to
various physical and chemical processes. Particles grow when different vapours condense
onto the particle surfaces. Due to their random Brownian motion in air, aerosol
particles collide with each other and stick or merge together in a process called coagulation.
Chemical reactions on the particle surface or inside the liquid phase change
the chemical composition of the particles. Finally, the particles are removed from the
atmosphere when they deposit on any available surfaces: on the ground, ocean and
lake surfaces, tree leaves, walls, windows, etc. In addition to dry deposition, particles
are washed out from atmosphere by falling rain droplets or snow flakes.
Atmospheric aerosols cover a wide range of particle sizes from molecular clusters close
to 1 nm to big dust or sea-salt particles of several µm in diameter. The upper size limit
is set by gravity, which makes large particles fall down rapidly. The aerosol number
concentration varies from a few 100 cm −3 in very clean Arctic areas (Koponen et al.,
2003) to several 100 000 cm −3 in polluted megacities (Mönkkönen et al., 2005; Wu
et al., 2008). The large range of variation is a challenge for instrumentation, as the
same instrument has to be capable of measuring three to four orders of magnitude
particle size range and even five orders of magnitude concentration range.
The lifetime of an aerosol particle in the lower atmosphere is on the order of one day
to one week (e.g. Williams et al., 2002). Despite their short lifetime, there is a persistent
aerosol population in the atmosphere, maintained by the continuous emission and
removal of aerosol particles into and out of the atmosphere. Due to different physical
processes — nucleation, particle growth by condensation, collisions between particles,
removal by gravitational settling or diffusion to surfaces — atmospheric aerosol has a
characteristic particle size distribution. Aerosol particles tend to center around some
particle sizes, thus forming different modes. Typically atmospheric aerosol has 3–4
modes: a nucleation mode around particle sizes ∼10–30 nm resulting from new particle
formation, an Aitken mode around 30–100 nm (named after a pioneer aerosol
scientist who first observed it), an accumulation mode around 0.1–1 µm, and a coarse
mode of large particles around 1–10 µm. The accumulation mode results from the
fact that for this size range the removal processes are slowest, making particles of this
size accumulate in the atmosphere (Laakso et al., 2003; Mammarella et al., 2011). In
addition, there is a persistent cluster mode at sizes 1–2.5 nm (Kulmala et al., 2007).
Due to their short lifetime, aerosol particles travel in the troposphere (lower part of the
atmosphere) typically some hundreds of kilometers, at maximum some thousands of
kilometers. Thus, in constrast to long-lived greenhouse gases, tropospheric aerosols are
not uniformly distributed around the globe, but are a local or regional phenomenon.
However, in the stratosphere aerosol particles (e.g. those emitted from volcanic eruptions)
survive much longer, having effects on weather and climate on longer time scales
Locally, aerosols affect air quality and deteriorate visibility (Chang et al., 2009a; Wang
et al., 2010). Elevated particle mass (PM) concentrations have been observed to correlate
with increased mortality in big cities (Dockery and Pope, 1994; Brunekreef and
Holgate, 2002; Peters and Pope, 2002). Based on these studies, regulations for safe
particle mass concentrations in size ranges < 10 µm (PM 10 ) and < 2.5 µm (PM 2.5 )
have been set up. Recently it has appeared more and more evidence, that especially
fine particles (< 2.5 µm) have negative health effects (Pope et al., 2002). While the
large (> 2.5 µm) particles deposit already in the nose and upper respiratory track, fine
particles can be transported far in our respiratory system and some of the ultrafine
particles (< 0.1 µm) may even enter the blood circulation system. It is expected, that
in the future there will be regulations not only for the particle mass but also for the
particle number concentration.
Despite their local nature, aerosols have regional and global effects on the weather and
climate (Mitchell et al., 1995; Haywood and Boucher, 2000; Lohmann and Feichter,
2005; Bennartz et al., 2011). Aerosol particles directly scatter and absorb solar and
infrared radiation, thereby affecting the amount of radiation reaching or escaping from
the Earth’s surface (the direct effect of aerosols) (Yu et al., 2006). Indirectly, aerosols
affect cloud formation by acting as cloud condensation nuclei (CCN) (Twomey, 1991;
Penner et al., 2004). Aerosols are crucial for cloud formation, because in the Earth’s
atmosphere the water vapour does not form droplets alone. Cloud droplets are formed
when water vapour nucleates (condenses) heterogenously on the surface of an aerosol
particle — thus every cloud droplet has an aerosol particle inside it. The amount of
aerosol particles available for cloud droplet formation affects the cloud cover as well as
the cloud properties: if there are more aerosols, there will be more but smaller cloud
droplets, as the same amount of water is divided to a larger number of aerosol particles.
Smaller cloud droplets reflect sunlight more efficiently i.e. make whiter clouds (first
indirect effect). Also, smaller cloud droplets are less eager to fall down as rain, and the
lifetime of the cloud will increase (second indirect effect).
From a climate point-of-view, the quantity of interest is the aerosols’ effect on the
radiative balance of the Earth (see Fig. 1). It is estimated that both the direct and
indirect effect have a total negative effect on the radiative balance (negative radiative
forcing): the more aerosols, the more sunlight will be reflected from aerosol particles
and clouds back to space. The absorption of sunlight and infrared radiation by aerosol
particles (especially black carbon aerosols) and cloud droplets (especially in high-level
clouds) causes a small warming effect, but in total the aerosol effect is estimated to be
cooling. TheIntergovernmental PanelonClimateChangereportgivesanestimate−0.5
W/m 2 for the direct and −0.7 W/m 2 for the indirect effect (IPCC, 2007). Overall, the
estimate for the total aerosol cooling effect (−1.2 W/m 2 ) is comparable to the warming
effect of CO 2 (1.66 W/m 2 ). However, the aerosol effect is associated with the largest
error bars (see Fig. 1), and the level of scientific understanding is stated to be low, in
contrast to greenhouse gases, whose effect is rather well understood. The research in
this thesis is one small contribution to quantify the aerosol effect more precisely, and
to reduce the uncertainty related to it.
In recent 20–30 years, considerable decreases in anthropogenic aerosol emissions have
happened in the Western countries, due to cleaning and filtering of the gas exhausts of
industry and transport systems (Hamed et al., 2010; Asmi et al., 2013). In the future,
this trend will continue, thus decreasing the man-influenced aerosol cooling effect. In
view of climate change, the major environmental problem of our time (Archer and
Pierrehumbert, 2011), this raises a concerning question: If the aerosol cooling effect
has been large, how much will the warming be accelerated, when the aerosol cooling
effect continues to decrease (Andreae et al., 2005; Arneth et al., 2009)? It is clear that
aerosols need to be taken into account in climate models when making predictions on
future climate change.
Measurements all around the world have shown that new particle formation seems
to occur almost everywhere on the Earth’s land-surface where aerosol measurement
instruments have been carried to (Kulmala et al., 2004d; Kulmala and Kerminen,
2008; Vakkari et al., 2011; Kyrö et al., 2013). Sulphuric acid has been identified as a
key compound in atmospheric particle formation and it participates both in nucleation
and particle growth. However, equally important for natural particle formation are
organic vapours, which contribute to particle condensational growth and account for
the major part of atmospheric aerosol mass (Jimenez et al., 2009; Riipinen et al.,
2011). The atmospheric aerosol is to some extent a self-regulating system: if there are
many particles emitted from other sources, such as pollution, there are less particles
produced by new particle formation; on the other hand, if the atmosphere is very clean
of particles, new particle formation occurs more frequently. Thus, atmospheric particle
formation maintains the aerosol particle population in the atmosphere.
Figure 1: Estimates for radiative forcing (RF) components for year 2005 (global averages).
Positive radiative forcing means a warming effect on climate and negative
radiative forcing a cooling effect. From IPCC (Intergovernmental Panel on Climate
Change) Fourth Assessment Report (IPCC, 2007).
Inoceanic areas andinrain forests inAmazonian, new particleformationin theboundary
layer occurs very rarely. There are still plenty of aerosols from other sources in
these environments, such as: sea salt particles and particles transported from the upper
atmosphere to the boundary layer on the oceans, biomass burning aerosols and
secondary organic aerosols in the Amazonian region, as well as particles from anthropogenic
One way to characterize aerosols is whether they are of natural or anthropogenic origin.
For primary aerosols, the origin is easily identified: sea salt, sand, pollen, bacteria,
viruses and other micro-organisms are examples of natural aerosols while all kinds of
pollution from combustion processes and biomass burning are examples of anthropogenic
aerosols. For secondary aerosols, the situation is not that easy. At first sight,
new particle formation could be called as natural, as it is happening ”naturally” in
the air — but new particle formation is to a large extent controlled by sulphuric acid,
which has both natural and anthropogenic sources. Sulphuric acid is formed in the atmosphere
mainly by oxidation of SO 2 , for which a major source is the burning of fossil
fuels. Volatile organic compounds, which condense on aerosol particles and constitute
most of the secondary aerosol mass, are mainly emitted by vegetation, but have also
anthropogenic sources (combustion of fossil fuels and other organicmatter). Thus, natural
and anthropogenic sources of particles and condensing vapours are mixed together
so that it is not fully possible to distinguish them. Also some natural primary emissions
are influenced by human activity: for example desertification increases emission
of mineral dust into air.
This thesis investigates atmospheric particleformationintheborealforest environment
by the methods of field data analysis and aerosol dynamical simulations. The main
emphasis is on studying the correlation of new particle formation with sulphuric acid
concentration. More specifically, this thesis aims to answer to the following research
questions or objectives:
• How arenew particle formationandgas phase sulphuric acid connected witheach
• To develop empirical parameterisations for the nucleation rate. What are the
values of the empirical nucleation coefficients indifferent environments and which
parameters do they depend on?
• Which factors, besides the nucleation mechanism, affect the correlation of the
particle formation rate with sulphuric acid?
• How accurate is the method used to calculate particle formation rate from the
size distribution data?
• What is the ability of aerosol particles in the boreal forest environment to act
as cloud condensation nuclei (CCN), and is new particle formation affecting the
These research questions are discussed in this introductory part and in the six articles
included in this thesis.
2 Atmospheric particle formation
from precursor vapours. The process is initiated by nucleation, in which small stable
clusters, of size 1–1.5 nm in ”diameter”, are formed. The precursor vapours must
be ”condensable”, i.e. they must have low saturation vapour pressures, so that the
vapours are eager to nucleate and stay in the condensed phase. The surrounding inert
gas is air, and air molecules do not participate in nucleation. The formed clusters grow
further by condensation of different vapours, eventually reaching sizes of 100–500 nm,
unless scavenged by the various aerosol removal processes. The upper size limit of
aerosol particles in atmosphere is set by gravitation: particles bigger than a few tens
of µm fall down rapidly due to gravitation.
background aerosol concentration (W. Birmili and A. Wiedensohler, 2000; Boy et al.,
2003; Birmili et al., 2003; Stanier et al., 2004; Lyubovtseva et al., 2005; McMurry et al.,
2005). Whileparticleformationfromgasphasecompounds (gas-to-particleconversion)
has been known to take place, and to be a source of new particles in the atmosphere,
already for a long time, it was only in late 1990’s that the whole process of atmospheric
particle formation was recorded for the first time (Weber et al., 1996; Mäkelä et al.,
1997). Since 1997, the continuous measurements of particle size distributions at the
Hyytiälä forestry field station (SMEAR II), from 3 nm to 500 nm and with 10 min.
time resolution, have shown that in boreal forest conditions new particle formation
occurs frequently all around the year, on 50–120 days per year (Aalto et al., 2001; Dal
Maso et al., 2005).
Figure 2 shows a typical example of a new particle formation event, measured by a
Differential Mobility Particle Sizer (DMPS) at the SMEAR II station in Hyytiälä,
Finland. Nucleation produces new 1–2 nm sized particles from gas-phase precursor
vapours, below the detection limit (diameter 3 nm) of the DMPS. After nucleation,
the clusters grow in size by condensation of vapours; these vapours can be the same or
different than the nucleating vapours. Due to their random Brownian motion in air,
the particles collide with each other and stick together, in a process called coagulation.
Due to condensation and coagulation, the new nucleation mode shifts to larger particle
sizes. When particles reach the size range > 50 nm (in diameter), they start to have
effects on climate: the particles can act as cloud condensation nuclei (CCN) i.e. be
seed particles for cloud droplets (Kerminen et al., 2012). The aerosol particles are
subject to these dynamical processes, until they are removed from the atmosphere by
gravitational settling and diffusion onto surfaces (dry deposition), or are scavenged by
falling rain droplets (wet deposition).
In the atmosphere, there is always a background aerosol distribution present. Often
simultaneously to or just before the start of nucleation, this background particle concentration
is decreasing due to the turbulent mixing initiated by sunlight warming the
ground in the morning. The onset of turbulent mixing increases the boundary layer
height (boundary layer = the lowest, turbulently mixed layer of the atmosphere), thus
Hyytiälä March 25 th 2003
0:00 06:00 12:00 18:00 24:00
10 100 1000 10000 100000
Concentration dN/dlog(d p
) (cm −3 )
Figure 2: An example of a new particle formation event measured by DMPS (Differential
Mobility Particle Sizer) at the SMEAR II station in Hyytiälä, Finland. The
surface plot presents the evolution of the particle size distribution with time on the
x-axis, particle diameter on the y-axis (log scale), and the normalized number concentration
indicated by the colour code. The aerosol dynamical processes modifying the
size distribution (at an exemplary location on diameter and time axes) are indicated.
mixing the particle-rich airmass of the boundary layer, left from the previous day, with
an upper airmass having a much lower particle concentration. This results in a remarkabledilution
of theparticle concentrations inthe morning hours (see Fig. 2). There are
observations that new particle formation is enhanced in conditions of strong turbulent
mixing (Nilsson et al., 2001; Lauros et al., 2007). However, it is not clear whether
the enhancement is due to turbulence itself or due to the decrease of the background
In continental areas, large amount of evidence shows that sulphuric acid (H 2 SO 4 ) participates
in both formation and growth of new particles. Sulphuric acid is thought
to be main nucleating compound, together with water and ammonia (see Sect. 2.2),
although some organic molecules may also participate in nucleation. Of the particle
the main part is accounted for by various organic vapours present in the atmosphere.
For example, in boreal forest conditions in Hyytiälä, the sulphuric acid contribution to
the observed particle growth rate (determined as GR = dd p /dt, where d p is the particle
diameter) is estimated to be 8–30 % (Boy et al., 2005). In polluted cities, where SO 2
and H 2 SO 4 concentrations are high, the sulphuric acid contribution is higher (34–65 %),
but even in those conditions it does not alone explain the particle growth (Yue et al.,
2010; Gao et al., 2011).
show a seasonal variation according to the growth season of the vegetation, implying
that organic compounds emitted by vegetation are important for particle growth (Hirsikko
et al., 2005; Yli-Juuti et al., 2011). A major source for condensable organic
vapours in the atmosphere are volatile organic compounds (VOCs) emitted by vegetation,
although anthropogenic VOC emissions also exist. The main biogenic VOC
groups are isoprene, monoterpenes and sesquiterpenes. In boreal forest areas, monoterpenes
(chemical formula C 5 H 10 , having several different molecular structures) emitted
from coniferous trees constitute the main part of VOC emissions (Haapanala et al.,
2007), while in deciduous forests isoprene is dominating (Carlton et al., 2009). The
VOCs do not condense directly on particles, since they are volatile i.e. have a high
saturation vapour pressure, but when VOCs are oxidised in the atmosphere by OH,
O 3 and NO 3 , semi-volatile reaction products having a lower saturation vapour pressure
are formed. The VOC oxidation chemistry is complex and the exact identities of
the condensable vapours are still unknown. However, these organic compounds have
recently been observed directly by in situ measurements of aerosol particle chemical
composition, showing that a major part of the aerosol mass is organic (Jimenez et al.,
2009; Laitinen et al., 2011; Zhang et al., 2011).
As a simple approximation, in aerosol science the formed particles are typically considered
to be liquid spheres, and mostly the modelling of aerosol formation is based on
this assumption. However, for very small clusters close to 1 nm one cannot accurately
determine the phase and diameter, and it would rather be more correct to speak about
a molecular cluster than a particle. From 3 nm upwards the number of molecules in
the particle is high enough, that we can speak of a ”macroscopic” particle, with a well
defined diameter and phase. For particles larger than 3 nm the assumption of spherical
liquid particles is usually good (excluding agglomerates of e.g. soot particles), based
on the typical temperatures in atmosphere and the fact that particles are growing
mainly due to condensation, thus making a liquid phase particle. However, there are
new observations which indicate that the phase of the formed particles is amorphous
(Virtanen et al., 2010), and it might be that the phase of aerosol particles needs to be
reconsidered in more detail in future studies.
In recent years, great advances in aerosol measurement technology have been achieved,
making it possible to detect the process of atmospheric nucleation directly from the
nucleation size at 1–2 nm (Zhao et al., 2010; Kulmala et al., 2012, 2013). However,
the details of atmospheric particle formation and particle growth are still not fully
2.1 Aerosol size distribution and its dynamics
The atmospheric aerosol particle population is described by the particle concentration,
size (diameter) and chemical composition. Typically, in physical studies of aerosols,
the chemical composition is neglected, and the aerosol is characterized by an aerosol
size distribution function, expressed either for the number concentration as the particle
number size distribution (mathematically denoted as dN(d p )/dd p or dN(d p )/dlog(d p ))
or for the mass concentration as the particle mass size distribution (dm(d p )/dd p ). The
atmospheric particle number size distribution peaks at small particle sizes, while the
mass distribution peaks at larger particle sizes as mass is proportional to the particle
volume (∼ d 3 p ) (see Fig. 3). The actual number or mass concentration (for a certain
size range and having units 1/cm 3 or µg/cm 3 ), is obtained by integration over the
desired size range.
In aerosol dynamical studies, most often we consider the number size distribution.
However, in air quality studies and the regulation standards for particulate pollution,
the mass concentration is used. In the following, the shortened term particle size
distribution means the particle number size distribution and the number concentration
has units 1/cm 3 . Due to the log-normal distribution with respect to particle size,
number concentration is most oftenexpressed inthe normalized formdN(d p )/dlog(d p ).
x 10 −17
) (1/cm 3 )
10 −9 10 −8 10 −7 10 −6 10 −5
Particle diameter (m)
) (µg/cm 3 )
Figure 3: An average particle number size distribution (red) and the corresponding
mass size distribution (black) in Kumpula, Helsinki, in springtime (Hussein et al.,
2004). The number size distribution consists of three modes, which are indicated by
dashed lines; for the mass distribution (assuming particle density of 1 g/cm 3 ) only the
total distribution is plotted.
The atmospheric aerosol size distribution is typically composed of 2–4 log-normally
distributed modes: a nucleation mode at < 30 nm, an Aitken mode at 30–100 nm,
an accumulation mode at 100 nm–1 µm and a coarse mode at 1–10 µm. Aitken and
accumulationmodesarealwayspresent intheatmosphere, withtheaccumulationmode
being the most persistent, because for that size range the removal mechanisms (dry
and wet deposition) are the slowest. The nucleation mode emerges on new particle
formation days and the strength of the coarse mode is dependent on primary emissions
of big particles, such as dust emissions. The atmospheric aerosol distributions differ in
different environments: in continental areas the distribution has 3–4 modes, whereas in
marine areas, where nucleation is rare, thedistribution isbi- or trimodal (e.g. Koponen
et al., 2002).
The aerosol size distribution is changing all the time due to various aerosol dynamical
processes, which modify particle concentrations, size and chemical composition. The
particles collide with each other and stick together, forming bigger particles or agglomerates,
in the process called coagulation. Particles grow by condensation of vapours
onto particle surfaces or shrink by evaporation of molecules from particle surfaces to
the gas phase. Nucleation inserts new, nm-sized particles into atmosphere, when condensable
vapours form new stable particles. Particles are removed from atmosphere
by dry and wet deposition: in dry deposition particles diffuse and stick to macroscopic
surfaces, e.g. tree leaves, or settle down to the Earth surface by gravitation; in wet
deposition particles are washed away from atmosphere as they collide with falling rain
droplets or with cloud droplets.
The processes mentioned above are the main aerosol dynamical processes acting in the
boundary layer. In clouds, aerosols may also undergo changes in size and chemical
composition. Every cloud droplet has an aerosol particle inside it (e.g. McFiggans
et al., 2006). Vapours and gases present in the cloud (such as nitric acid, sulphur
dioxide, organic compounds and water) condense or dissolve to particles, and after that
the compounds undergo chemical reactions in the aqueous phase. When the prevailing
ambient conditions change, some amount of condensed material may evaporate from
the particle, leaving the seed particle composition and size changed in comparison to
the original state (e.g. Romakkaniemi et al., 2006). This is called cloud processing
of aerosol particles. A special bimodal structure of aerosol size distributions, often
encountered in marine boundary layer, is related to several cloud processing cycles of
aerosol particles (Hoppel et al., 1996).
In addition to these physical processes, there may be surface reactions or heterogenous
nucleation (nucleation on top of an existing particle) that change the particle size and
composition. Chemical reactions and polymerisation processes inside the particle can
modify the chemical composition and stability of the aerosol particle (aging of aerosol).
2.1.1 Condensation and coagulation
Because the size distribution of aerosol particles spans from the molecular scale (diameter
of few nm) to microscopic scale (diameter of few µm), different theoretical frameworks
are needed: small nm-sized particles are in the free-molecular regime, where
particles behave similarly to gas molecules, whereas large particles are in the continuum
regime, where particle experiences the surrounding gas as a continuous fluid. In
the continuum regime, both condensation and coagulation in aerosol systems are dealt
with the aid of diffusion theory. With condensation the use of diffusion theory is selfevident,
but also coagulation in the continuum regime can be considered as a diffusion
process: small particles in a fluid are diffusing towards a big (stationary) particle. In
the free molecular regime, the kinetic gas theory applies both for condensation and
coagulation. In between these, there is a transition regime, in which both diffusive and
free-molecular effects are important.
The condensation or evaporation flux is governed by the equilibrium vapour pressure
(or concentration) prevailing at the particle surface. On the curved particle surface,
the equilibrium pressure is always higher than on a planar surface of the same composition,
because of weaker atomic bonding between surface molecules/atoms on a curved
surface. This curvature effect on the equilibrium (saturation) vapour pressure is called
the Kelvin effect and it is determined by the Kelvin equation:
( 4Mv σ
p eq = p sat exp , (1)
where p sat is the vapour saturation pressure for a planar surface, M v is the molar mass
of the vapour, σ is the surface tension of the liquid, R is the universal gas constant,
T is temperature, ρ is the density of the liquid and d p is the diameter of the liquid
particle (Seinfeld and Pandis, 2006; Vehkamäki, 2006).
The difference between the vapour concentration far from the particle and the equilibrium
concentration at the particle surface determines the direction and magnitude of
the mass flux towards/from the particle (I m ∝ (c vapour −c eq )). The Kelvin effect limits
the condensation of vapours on a curved surface: the smaller the particle diameter, the
more eagerly the molecules evaporate from the particle surface.
Due to the Kelvin effect, the condensation onto small, few-nm sized particles, would
be extremely difficult for most of the condensable vapours (e.g. oxidation products of
VOCs) present in the atmosphere. Sulphuric acid is the exeption: it has a very small
saturation vapour pressure (< 10 −4 Pa, Ayers et al., 1980; Marti et al., 1997), so that
even with the Kelvin effect the saturation vapour pressure remains negligible, and it
starts to condense on particles directly after nucleation. However, also for the smallest
particles, the particle growth rate is explained only partly by sulphuric acid, and the
rest of the growth is attributed to various organic compounds (Riipinen et al., 2012).
To theoretically explain the organic vapour contribution on the particle growth rates,
where p sat,org is the organic vapour saturation pressure, γ org is the activity coefficient
of the organic substance, x org its molar fraction, M org the molecular mass and ρ org
the density. This mechanism for organic vapour condensation was applied in aerosol
dynamical simulations of paper III.
In the atmosphere, coagulation is caused by random Brownian motion of aerosol particles.
Due to velocity differences, both in direction and magnitude, particles collide
with each other. For aerosols, the collisions are assumed to be non-elastic, i.e. particles
alwayssticktogether. Often, thecollisionisassumedtobebetween liquidspheres, making
the particles merge together, thus forming a new, slightly larger spherical particle
(agglomeration is not taken into account). The collision frequency function (= coagulation
coefficient) can be derived from diffusion theory for the continuum regime and
from kinetic gas theory for the free molecular regime particles, and it depends strongly
on particle sizes. Coagulation is most efficient between particles of big size difference:
the large particle surface collects the small, rapidly moving particles. Therefore, coagulational
scavenging to backgound aerosol (at around 100–500 nm) is the main loss
mechanism for small, nucleation mode particles. The coagulation coefficient is smallest
and rather independent on particle size for the particles of equal size (Seinfeld and
In addition to Brownian motion, velocity differences resulting from gradients in air
flow, electrical or gravitational force field can cause collisions between particles. These
processes, however, are important only at high velocity or force gradients occuring e.g.
in flow tubes and are not significant coagulation processes in the atmosphere.
Thetheoryregime forcondensation andcoagulationisdefined bytheKnudsen number,
which describes the nature of the suspending fluid relative to the particle:
Kn = 2λ air
where λ air is the mean free path of air molecules (about 65 nm at T = 298 K and p
= 1 atm) and d p is the particle diameter. When Kn >> 1, aerosol particles experience
collisions similarly as molecules and we are in the kinetic regime. In this regime,
the kinetic gas theory applies. When Kn
With coagulation, thequantities to be compared arethe mean free path of thediffusing
aerosol particle (smaller particle, λ p ) and the diameter of the absorbing particle d p .
However, the mean free path of aerosol particles is only weakly dependent on particle
size, and the value is quite close to the air mean free path (λ p varies between 10–60 nm;
Seinfeld andPandis (2006, Table 8.5)). Because ofthat, thesamedefinition ofKnudsen
number (Eq. 3) can be used also in the case of coagulation to roughly characterize the
theory regime. In exact calculations, the different equations for transition regime and
free molecular coagulation coefficient use slightly different expressions for the Knudsen
number (Seinfeld and Pandis, 2006). The most widely used formula for the coagulation
coefficent (which is also used in this thesis) is the one by Fuchs (1964).
2.1.2 General dynamical equation
containing terms for all aerosol dynamical processes acting on the aerosol population.
The general dynamic equation (GDE), expressed in the volume space v = 1 6 πd3 p, reads
(Seinfeld and Pandis, 2006):
= 1 2
K(v −q,q)n(v −q,t)n(q,t)dq−n(v,t)
∂v [I(v)n(v,t)]+J nucδ(v −v nuc )+S(v)−R(v), (4)
where n(v,t) = ∂N(v,t)/∂v is the particle size distribution function, t is time and
v is the particle volume, K(v,q) is the coagulation coefficient between particles of
volume v and q, I(v) is the total volume flux of vapour molecules onto the particle
due to condensation/evaporation, J nuc is the nucleation rate, v nuc is the volume of
the nucleated particle and δ(v − v nuc ) is the delta function, with a value of unity for
v = v nuc and otherwise zero. The first two terms on the right hand side represent
coagulation (production of v-sized particles in collisions of smaller particles and the
termrepresents condensational growthorshrinkageduetoevaporation, thefourthterm
represents nucleation, and S and R are possible additional source and removal terms.
In practice, the general dynamic equation is often used in a discrete form, as we deal
with measured discrete spectrums or utilize models with a sectional representation for
aerosol size distribution. In modal models, which express the aerosol size distribution
as a superposition of continuous log-normal modes, the GDE is used in the continuous
form of Eq. 4. In models, the GDE is integrated numerically to solve the particle size
distribution evolution. In aerosol studies, particles are often assumed to be spherical,
and the GDE can then be expressed more conveniently with the particle diameter.
2.1.3 Condensation and Coagulation sinks
Two useful quantities – the condensation sink and the coagulation sink – have been
introduced to characterize the aerosol size distribution in terms of condensation and
coagulation with one scalar quantity (Kulmala et al., 2001a).
The condensation sink (CS) describes the condensation rate of vapour onto the whole
particle size distribution:
vapour loss rate due to condensation = CS ×C v , (5)
where C v is the concentration of condensable vapour, i.e. the condensation sink is the
vapour condensation rate per one molecule and has units 1/s.
The equation for the condensation sink can be derived from condensation theory. It
depends on the background particle size distribution (particle surface area) and vapour
diffusion properties (Kulmala et al., 2001a):
CS = 2πD v β m (d p )d p n(d p )dd p
∼ = 2πDv β m (d p,i )d p,i N i , (6)
where D v is the diffusion constant of the vapour, n(d p ) is the particle size distribution
function, d p is the particle diameter, and the integration is performed over the whole
particle size distribution. The latter form is for a discrete particle size distribution
N i (d p,i ). Because thediffusionconstant isvapour-specific, theCS hastobedetermined
for a specific vapour, typically for sulphuric acid (H 2 SO 4 ). The parameter β m (d p ) is the
Fuchs-Sutugin correction factor forthe transition regime mass flux (Fuchs andSutugin,
β m =
where Kn is the Knudsen number and α m is the mass accommodation coefficient.
With the Fuchs-Sutugin transitional regime correction factor, Equation 6 is valid for
allparticle sizes, fromkinetic to continuum regime; the semi-empirical correction factor
takes into account the changes in the condensation theory when particle size decreases.
The mass accommodation coefficient α m is also called ”a sticking coefficient” and it
describes the probability that a molecule, when hitting a particle surface, sticks onto
it. There has been quite much debate about the value of α m (Jefferson et al., 1997).
In most cases, it is assumed to be unity (α m = 1), meaning that when a molecule hits
a surface, it will be absorbed.
Analogously to the condensation sink, the coagulation sink is defined for a certain
particle size as the loss rate due to coagulation per one particle. For a discrete size
distribution this is expressed as:
Coagulation rate of particles of diameter d i = CoagS di ×N i ,
where CoagS di is the coagulation sink (unit 1/s) and N i is the number concentration
of particles in a size bin around particle diameter d i . The formula for coagulation sink
can bederived fromthe equation for Brownian coagulationrate, giving (Kulmala et al.,
CoagS(d p,i ,t) =
β(d p,i ,d ′ p)n(d ′ p,t)dd ′ p ∼ = ∑ j
β(d i ,d j )N j , (8)
where β(d p,i ,d ′ p) is the Brownian coagulation coefficient i.e. the collision frequency
function between particles of diameters d p,i and d ′ p (Seinfeld and Pandis, 2006). The
sum expression on the right is the formula for discrete size distribution.
Typically the coagulation sink is calculated for small nucleation mode particles, as
for nucleation mode particles. The coagulation rate and thus CoagS is largest for the
smallest particles, and decreases as the particle size increases (Dal Maso et al., 2002).
For small particles of d p = 1 nm the coagulationsink approaches the condensation sink,
because condensation can be viewed as collisions (= coagulation) of H 2 SO 4 molecules
(having ”diameter” below 1 nm) with background particles.
Some researchers have used the concept of Fuchs surface area instead of condensation
A Fuchs = 4π 3
Knβ m (d p )d 2 pn(d p )dd p , (9)
the meaning is analogous to the condensation sink (McMurry and Friedlander, 1978;
McMurry et al., 2005). Connecting this with the equation for CS (Eq. 6) and applying
λ v = 3D v /¯c v for the mean free path in Kn (Seinfeld and Pandis, 2006), a relationship
between the condensation sink and the Fuchs surface area A Fuchs can be derived:
CS = 1 4 ¯c vA Fuchs , (10)
where ¯c v is the mean thermal velocity of the condensing vapour molecule.
The condensation and coagulation sinks are useful quantities to descibe the particle
size distribution with a one scalar quantity. Both are measures of total aerosol surface
area, the former in the view of condensation and the latter in view of coagulation. The
value of CS and CoagS is determined especially by the concentration of large particles,
which have a large surface area.
In new particle formation studies, CS is often used instead of CoagS, even if one
actually, inaconceptualsense, isreferringbothtothecondensationandthecoagulation
actually means that both the CS and CoagS are low, having two effects favouring
nucleation: i) there will be more vapour available for nucleation and condensational
with large particles will be smaller (low CoagS).
2.2.1 Basic concepts of nucleation theory
By definition, nucleation is the first step of a phase transition process (Vehkamäki,
2006). All phase transitions start with nucleation. For example, freezing of water
typically starts with nucleation of small ice crystals around impurities present in water
(molecules, small particles). These crystals then grow in size and result in macroscopic
freezing of the water, if the temperature stays below zero. Similarly, boiling of water
begins with bubble formation (= nucleation of gas phase bubbles from liquid phase)
around impurities dissolved in water or present on the inner surface of the stewpot.
These are examples of heterogenous nucleation, in which nucleation happens on top of
a foreign surface, such as the surface of a small impurity particle. In distilled water,
which is free from impurities, nucleation (such as formation of ice crystals or bubbles)
happens homogenously without the aid of an exisiting surface. Homogenous nucleation
isalways energetically moredifficult thanheterogenous nucleation; therefore freezing of
distilled water requires lower temperatures and boiling happens at higher temperatures
than for normal water with impurities.
In atmospheric particle formation, we consider the transition from gas phase to liquid
or solid phase, i.e. the nucleation of liquid or solid phase clusters from gas-phase
precursors. Typically, for simplicity, the phase of the formed cluster or particle is
considered to be liquid.
As all physical processes in nature, nucleation is governed by energy. For nucleation
to happen, the energy state of a nucleated, liquid phase particle must be lower than
the initial state of vapour molecules. The first requirement for this is, that the vapour
is supersaturated. The saturation ratio S i (for vapour i) is defined as:
S i = p i,v
where p i,v is the partial pressure of vapour i (in air) and p i,sat is its saturation vapour
pressure. The vapour is supersaturated when S i > 1, meaning that there is an excess
amount of molecules in the vapour phase and the liquid state would be energetically
Innucleation, in between the initial (vapour) andfinal (nucleated cluster) energy states
there is an energy barrier which needs to be crossed with the aid of thermal energy.
In classical nucleation theory, the probability of crossing the barrier is given by the
Boltzmann factor e −∆G/k BT (∆G is the height of the energy barrier, k B is Boltzmann’s
constant and T is temperature), and the nucleation rate is:
J nuc = K kin e −∆G∗ /k B T . (12)
In this equation ∆G ∗ is the Gibbs free energy of the formation of the critical cluster (=
height of the energy barrier) and K kin is a kinetic prefactor accounting for the collision
rate of vapour molecules with the cluster, which make the cluster grow. According
to classical nucleation theory the Gibbs free energy (for homogenous nucleation) is
(Seinfeld and Pandis, 2006; Vehkamäki, 2006):
∆G = −nk B T lnS +4πr 2 σ, (13)
where n is the number of molecules in the cluster, r is the cluster radius, S is the
saturation ratio of the vapour and σ is the surface tension. The first term represents
the gain in energy that is obtained in forming a liquid phase cluster, and the second
term is the energy needed to create a new surface (due to surface tension). The typical
form of the Gibbs free energy curve is shown in Figure 4, where the maximum of the
curve represents the critical point: the smallest stable cluster i.e. the critical cluster,
that does not tend to evaporate (radius r ∗ at saturation ratio S ∗ ). The clusters bigger
than r ∗ start to grow spontaneously by condensation, as the cluster moves downhill on
critical cluster sizes are ∼1–5 nm, number of molecules being from a few molecules to
∼100. In multicomponent nucleation, involving more than one compound, the Gibbs
free energy becomes a surface with i dimensions, i being the number of compounds.
Depending on the substances, multicomponent nucleation can be either easier or more
difficult than homogenous nucleation of the participating substances.
In deriving the equation for ∆G, several approximations were made. For example, the
cluster is assumed to be a liquid sphere, and it is assumed to have the properties (density,
surface tension) of bulk liquid. It is clear that these approximations are very rough
and do not hold very well for clusters of a couple of nanometers in diameter (Merikanto
et al., 2007). Despite its deficiences, classical nucleation theory is so far the best concise
theory for nucleation and it is useful in interpretation of experimental studies on
nucleation. In many cases the classical nucleation theory predicts the S-dependence
right but T-dependence wrong, suggesting that the theory predicts the size of critical
cluster correctly, but fails in describing the energy of the cluster (Vehkamäki, 2006).
For molecular clusters, ab initio quantum chemical calculations provide physically and
chemically more accurate description, and can give insights on the structure of nucleated
clusters (Kurtén et al., 2007; Torpo et al., 2007; Kurtén et al., 2008; Ortega et al.,
S = 0.9
S = 1.0
Gibbs free energy (J)
1 x 10−16 Radius (m)
S = 1.1
S = 1.15
0 0.5 1 1.5 2
x 10 −8
Figure 4: The Gibbs free energy curves for homogenous nucleation of water vapour at
four different saturation ratios. The Gibbs free energy has a maximum and nucleation
is possible when S > 1. The critical cluster size r ∗ and the corresponding energy of
the critical cluster (G ∗ ) at the maximum of the ∆G curve are indicated.
One of the most useful theoretical results for nucleation is the nucleation theorem. The
first nucleation theorem states, that the derivative of the logarithm of nucleation rate
with respect to the logatrithm of saturation ratio is related to the number of molecules
in the critical cluster (Vehkamäki, 2006):
= n ∗ i +1 ≈ n∗ i , (14)
where J nuc is the nucleation rate, S i is the saturation ratio of the nucleating vapour,
and n ∗ i is the number of molecules of this substance in the critical cluster. In multicomponent
nucleation, the nucleation theorem applies separately for each nucleating
The first nucleation theorem is a general result and not restricted to any special nucleation
theory; thus it is valid more widely than the classical nucleation theory. In
principle, it applies for any nucleation process which has an energy barrier associated
with it. Therefore, it is very useful in interpretation of nucleation experiments. By
measuring the nucleation rate (J nuc ) as a function of saturation ratio (S i ) of a vapour,
and plotting the results on log-log axes, the slope gives the number of molecules of that
vapour in the critical cluster.
Besides laboratory measurements, the nucleation theorem has been applied in connection
of field measurements of atmospheric nucleation to predict the size of the critical
cluster (e.g. papers I–II). Just recently, there are new results that indicate that the
nucleation theorem may not hold in conditions in which there are local minima in the
Gibbs free energy surface (Vehkamäki et al., 2012). In that case, the conclusions on
the number of molecules should not be made based on the slope of log(J nuc ) vs. log(S i )
curve. So far, it is not known how the Gibbs free energy looks like in atmospheric nucleation.
However, a local minimum would be expected in atmospheric nucleation, as a
stable pre-nucleation cluster pool is observed to exist in field measurements (Kulmala
et al., 2007).
sink of the background aerosol may affect the interpretation of the results.
2.2.2 Atmospheric nucleation mechanisms
A wide range of experimental and theoretical evidence shows that sulphuric acid
(H 2 SO 4 ) is involved in atmospheric particle formation. In atmospheric aerosols, sulphate
is always observed, even if organic compounds often form the dominant part of
the aerosol mass (e.g. Jimenez et al., 2009). Sulphuric acid has low saturation vapour
pressure (< 10 −4 Pa, Ayers et al., 1980; Marti et al., 1997), which makes it eager to
nucleate and stay in the condensed phase in atmospheric conditions. Sulphuric acid
co-nucleates efficiently with water vapour, which is abundant in the atmosphere. Even
small amounts of H 2 SO 4 cause a huge increase of water nucleation rates in laboratory
experiments (Doyle, 1961).
On the basis of classical nucleation theory, two mechanisms for atmospheric nucleation
have been proposed: binary homogenous nucleation of sulphuric acid and water (Kulmala
et al., 1998a; Vehkamäki et al., 2002) and ternary nucleation of sulphuric acid,
water and ammonia (Korhonen et al., 1999; Napari et al., 2002a,b; Anttila et al., 2005;
Merikanto et al., 2007). Based on the acid-base interactions between the molecules (in
solution ammonia lowers the equilibrium vapour pressure of sulphuric acid), ternary
H 2 SO 4 -NH 3 -H 2 O nucleation happens easier (i.e. at lower saturation ratios) than binary
H 2 SO 4 -H 2 O nucleation; and both binary and ternary nucleation happen easier
than homogenous nucleation of H 2 SO 4 .
Binary H 2 SO 4 -H 2 O nucleation predicts nucleation rates well in the free troposphere
(Spracklen et al., 2005), but fails to expain nucleation in the boundary layer (e.g.
Spracklen et al., 2006; Chang et al., 2009b). However, lacking better nucleation theories,
binary H 2 SO 4 -H 2 O and ternary H 2 SO 4 -NH 3 -H 2 O nucleation theories have been
used widely to calculate nucleation rates in aerosol dynamical box models and global
models. In applying the theories, sometimes a correction factor has been used in order
to get the nucleation rates closer to the observed particle formation rates (Jung et al.,
2008). Ternary nucleation has been shown to work reasonably well in predicting the
occurence of nucleation events in polluted cities with high concentrations of sulphuric
acid and ammonia, but in terms of particle number it seems to produce too intense
nucleation events (Gaydos et al., 2005; Jung et al., 2008).
It has also been proposed that atmospheric nucleation could be purely kinetic i.e.
happen without any energy barrier (McMurry and Friedlander, 1979). In that case,
the nucleation rate would be determined only by the kinetic collision rate between
the molecules (with ∆G = 0 in Eq. 12), assuming that every collision results in the
formation of a stable cluster. For example, the rate of homogenous, barrierless kinetic
nucleation of sulphuric acid would equal the collision rate of H 2 SO 4 molecules. The
kinetic collision rate between molecules a and b is given by the equation (McMurry and
Friedlander, 1980; Seinfeld and Pandis, 2006):
K kin =
( 8kB T
+r b ) 2 , (15)
where r a and r b are the radii of the reactant molecules and m ab = m a m b /(m a + m b )
is their reduced mass, T is temperature and k B the Boltzmann’s constant. The term
( 8k BT
) 1/2 is the relative mean thermal velocity of the molecules and π(r a + r b ) 2 their
collision cross section. For H 2 SO 4 molecules at room temperature, the kinetic collision
rate is about 3 ·10 −10 cm 3 s −1 . The kinetic collision frequency sets the absolute
maximum for the possible nucleation rate in a system.
In atmospheric field measurements, a striking observation is that nucleation rates are
observed to correlate with sulphuric acid to the power between 1–2 (Weber et al., 1996;
Birmiliet al.,2000;Fiedler etal.,2005;Kulmalaet al.,2006, paper IandII).Thisisin
contradictionwithbinaryandternarynucleationtheories, whichpredict thecorrelation
exponents of > 10 and 5–10, respectively (Kulmala et al., 1998a; Vehkamäki et al.,
2002). In case of classical, homogenous nucleation with a simple form for the Gibbs
free energy curve, the correlation exponent corresponds to the number of molecules
in the critical cluster (Eq. 14, Vehkamäki et al., 2012). The slope of 2 was first
observed by Weber et al. (1996) and reported also by Birmili et al. (2000), but at that
time the observation did not recieve wider attention. Later, by H 2 SO 4 concentration
measurements at the Hyytiälä SMEAR II station, this connection was rediscovered
(Fiedler et al., 2005; Kulmala et al., 2006). In papers I–II this connection and its
implications were studied in detail.
The failure of binary and ternary nucleation theories, and the observation that particle
formation rates correlate simply with the first or second power of the sulphuric acid
concentration (J nuc ∝ [H 2 SO 4 ] n , with n = 1–2), has led scientists to develope empirical
parameterisations for the nucleation rate. These parameterisations, namely activation
and kinetic nucleation, were developed in papers I and II. They have been applied
quite widely in aerosol models (e.g. Spracklen et al., 2006) and been further developed
by Paasonen et al. (2009, 2010).
The correlation exponent (the slope of log(J nuc ) vs log([H 2 SO 4 ]) plot) has been taken
to represent the number of molecules in the critical cluster (see Eq. 14). Thus, atmospheric
observations have been interpreted so, that the critical cluster contains only
few (1–2) sulphuric acid molecules (papers I–II). However, this is too strong a conclusion
to make: as Vehkamäki et al. (2012) pointed out, if the Gibbs free energy curve
has a local minima at pre-nucleation sizes, the simple form of the nucleation theorem
(Eq. 14) is not valid. Thus, the correlation exponent n should not be interpreted
as the number of molecules of that kind in the critical cluster, but rather as giving
information about the rate limiting step in atmospheric nucleation. According to the
results of paper I and II, this rate limiting step is proportional to the sulphuric acid
concentration to the power 1–2.
Ion-induced nucleation, i.e. nucleation initiated by charged clusters, and ion-mediated
nucleation, including also the formationofneutral clusters by recombination of positive
and negative ions, have also been proposed as possible nucleation mechanisms in the
atmosphere (Yu and Turco, 2000). There is a constant charged cluster pool (of both
polarities) observed to exist in the atmosphere, and ion events similar to neutral new
particle formation events are observed (Kulmala et al., 2007; Hirsikko et al., 2011).
Theoretically, the presence of ions should enhance nucleation by introducing a local
minimum to the Gibbs free energy curve and by lowering its maximum. According to
current knowledge, ion-induced nucleation is expected to have only a minor contribution
to particle formation in the boundary layer, but possibly has some importance
in nucleation in the mid-troposphere (Hirsikko et al., 2011; Kirkby et al., 2011); although
some contradicting opinions also exist (Yu et al., 2008, 2010). In boreal forest
conditions, the contribution of ions to nucleation has been estimated to be about 1–10
% (Manninen et al., 2009; Gagné et al., 2010, 2012), while in other environments the
fraction has been observed to vary in the range 0.5–27 % (Manninen et al., 2010).
Incoastal areas, suchasMaceHeadinIreland, particleformationisobserved tohappen
through nucleation of iodine dioxide (OIO), emitted by algae when exposured to direct
sunlight (O’Dowd et al., 2002; O’Dowd and Hoffmann, 2005; Vuollekoski et al., 2009).
2.2.3 Laboratory measurements of atmospheric nucleation
In laboratory studies, performed mainly for the H 2 SO 4 -H 2 O system, it has been extremelydifficult
toobserve nucleationatconditionsmimicing theatmosphere(Viisanen
et al., 1997; Ball et al., 1999; Young et al., 2008; Benson et al., 2008; Brus et al., 2010).
Berndt et al. (2005) presented the first results of laboratory measurements, in which
nucleation was observed at close to atmosheric concentrations of sulphuric acid and
slopes approaching the atmospheric value of 2.
The comparison of various laboratory measurements and atmospheric measurements
(QUEST II, paper I) is presented in Figure 5 (Brus et al. 2010). Summarizing,
in the first decade of 2000’s, there were three discrepancies found in almost all laboratory
studies of H 2 SO 4 -H 2 O nucleation: i) The onset of nucleation requires much
higher concentrations than observed in the atmosphere. ii) The slope of the log(J)
vs log([H 2 SO 4 ]) plot is much higher than observed in the atmosphere, typically in the
range 4–8. iii) The results are sensitive to the production method of H 2 SO 4 : the nucleation
rates were much higher (or onset of nucleation happened at many orders of
magnitude lower concentrations) if H 2 SO 4 was produced in situ by reaction of SO 2 and
OH than if the H 2 SO 4 was evaporized from a liquid H 2 SO 4 sample. Especially the last
observation (iii) of high nucleation rates for in situ production of H 2 SO 4 as compared
to the liquid source was considered as a big mystery (Berndt et al., 2005; Brus et al.,
10 5 atmospheric (0 °C)
from liquid samples
[cm -3 s -1 ]
from OH + SO 2
10 5 10 6 10 7 10 8 10 9 10 10 10 11
] [cm -3 ]
this work RH = 10,30,50%
Viisanen et al. RH = 38.2 and 52.3%
Wyslouzil et al. RH = 14 and 28%
Berndt et al. RH= 11,22,42,60%
Young et al. RH = 11,15,23%, 100 ppm
Young et al. RH = 15%, 1 ppm
Ball et al. RH = 2.3,4.7,7.5,15.3%,
Sihto et al. (2006) - atmospheric nucleation - Quest 2
Figure 5: Homogenous nucleation rate as a function of sulphuric acid concentration
for binary H 2 SO 4 -H 2 O system, obtained from different laboratory measurements and
comparison with the atmospheric data from the QUEST II campaign at the Hyytiälä,
SMEAR II station (paper I). Reprinted by permission from Brus et al. (2010).
2010). It led scientists to propose theories, that the nucleating agent would be some
other reaction product in the SO 2 +OH reaction pathway (see Sect. 2.3), such as HSO 3
or HSO 5 (Berndt et al., 2008; Laaksonen et al., 2008; Salonen et al., 2009).
In 2010, all three mysteries were solved at the same time by Sipilä et al. (2010). They
performed new laboratory measurements in a laminar flow tube applying novel measurement
technology for detection of small particles down to ∼ 1.3 nm: pulse-heightanalyzing
ultrafine-condensation particle counter (PHA-UCPC, Sipilä et al., 2009) and
particle size magnifier (PSM, Vanhanen et al., 2011). With these intstruments, nucleation
of H 2 SO 4 and H 2 O was observed at atmospheric conditions (onset of nucleation
at H 2 SO 4 concentration ∼ 10 6 cm −3 ) and with a slope 1.6–1.9.
The high onset H 2 SO 4 concentrations for nucleation and steep slopes of the log(J) vs
log([H 2 SO 4 ]) plot reported in earlier studies were explained to be caused by improper
instrumentation, which was not able to measure close to 3 nm sized particles with a
sufficient efficiency. The ultrafine condensation particle counter (UCPC, TSI 3025),
which was used in many studies, has a steeply rising counting efficiency at 3–6 nm.
This caused nucleation rates at different H 2 SO 4 concentrations (having also different
particle growth rates after nucleation) to be measured with different counting efficiencies,
resulting in an apparent increase of the nucleation rate with H 2 SO 4 concentration
and a high slope of the log(J) vs log([H 2 SO 4 ]) curve. Thus, in addition to the importance
of a suitable detector, also the growth rate (determined by H 2 SO 4 concentration
and residence time in the flow reactor) affects the results. Many earlier experiments
were performed with rather short residence times, resulting in a small growth rate, and
a large fraction of particles remaining so small that they were not counted.
The difference between liquid source and production of H 2 SO 4 from SO 2 +OH reaction
(”the sulphuric acid mystery”) was explained by different concentration profiles (as
a function of time) between these two cases: with a liquid, point-like instantaneous
source the concentration of H 2 SO 4 decreased steeply after nucleation, whereas in-situ
production yielded quite constant H 2 SO 4 concentration as long as the OH source (UVlight)
was on. In the former case, the growth rates were smaller than in the latter
case, resulting in a considerable fraction of nucleated particles not reaching a size big
enough to be detected.
In summary, proper instrumentation and high enough growth rates are required in
order to obtain correct results in nucleation experiments. Especially the Particle Size
Magnifier (PSM), which has close-to-unity counting efficiency for small particles, has
made it possible measure nucleation rates with good accuracy. It is possible that all
earlier laboratory experiments of nucleation are affected by the errors sources pointed
out by Sipilä et al. (2010), and therefore earlier laboratory results on sulphuric acidwater
nucleation should be interpreted with care.
Current thinking on atmospheric particle formation is as follows (Kulmala et al., 2013).
A more or less constant neutral cluster pool at 1–2 nm is observed to exist in the
atmosphere (Kulmala et al., 2007). Under certain, partly yet unidentified, conditions
these pre-critical clusters start to grow to bigger sizes. This happens normally during
daytime, with the participation of condensable vapours produced by photo-oxidation.
The most important vapour forinitiation ofthe growthof pre-nucleation clusters seems
to be sulphuric acid. Simultaneously with sulphuric acid, organic vapours start to
condense, possibly with the nano-Köhler mechanism, and speed up the particle growth
2.3 Formation and loss processes of sulphuric acid in the
Gas-phase sulphuric acid is produced in the atmosphere mainly through oxidation of
sulphur dioxide (SO 2 ) by OH radicals. The main sources of sulphur dioxide in today’s
atmosphere are emissions from fossil fuel burning and industry, global estimate for
emissions being 70 Tg(S)/year (Seinfeld and Pandis, 2006). Naturally SO 2 is emitted
from volcanic eruptions (global estimate 7–8 Tg(S)/year) and forest fires (global estimate
for emissions from biomass burning 2.8 Tg(S)/year) (Seinfeld and Pandis, 2006).
Over oceans, which lack extensive anthropogenic sulphur emissions, dimethylsulphide
(CH 3 SCH 3 , DMS) is the dominant source for SO 2 . DMS is produced by phytoplankton
and other marine organisms in the ocean and emitted into the atmosphere, where it
reacts with OH radicals and forms SO 2 (among other compounds). Altogether, DMS
is the largest natural contributor to the global sulphur flux into the atmosphere with
global emissions of 15–25 Tg(S)/year (Seinfeld and Pandis, 2006).
In the atmosphere, SO 2 reacts with hydroxyl radical (OH) in a sequence of reactions,
eventually forming sulphuric acid (e.g. Reiner and Arnold, 1994):
SO 2 +OH·+ M → HOSO 2 ·+ M (16)
HOSO 2 ·+ O 2 → HO 2 ·+ SO 3 (17)
SO 3 +H 2 O+ M → H 2 SO 4 + M. (18)
Here M represents a non-reactive molecule of the surrounding gas (in air typically N 2
or O 2 ), which is taking the excess energy released in the reaction. According to present
knowledge, this is the main mechanism for production of gas phase sulphuric acid in
the atmosphere. The second and third reaction (17 and 18) are fast, so that the rate
limiting step in thereaction scheme is reaction16. Thus the formationrateof sulphuric
acid is given by the rate of reaction 16: k 16 [SO 2 ][OH], where k 16 is the reaction rate
Hydroxyl radicals (OH·), in turn, are formed in photodissociation of ozone (O 3 )
molecules by ultraviolet (UV-B) radiation. The reaction mechanism is as follows:
O 3 +hν → O 2 +O,(λ < 1180 nm) (19)
→ O( 1 D)+O 2 ,(λ < 320 nm, UVB) (20)
O( 1 D)+H 2 O → 2 OH· , (21)
where O( 1 D) is the exited singlet state of the oxygen atom. This formation process
makes the OH concentration vary according to the intensity of UV-B radiation. The
formation depends also on the water vapour concentration ([H 2 O]), but the effect is
to the solar UV radiation. OH is a highly reactive radical, with a lifetime of about 1
second, which reacts with almost all chemically reactive compounds in the atmosphere.
Despite the variety of loss processes for OH, the total OH concentration has been
observed to follow UV radiation with a good accuracy, both on diurnal and seasonal
time scales (Rohrer and Berresheim, 2006). Therefore, simply the intensity of UV
radiation can be used in modelling as a proxy for OH concentration, just scaled to a
proper maximum value (of the order 10 5 cm −3 –10 6 cm −3 ).
Owing to the high reactivity and short lifetime of OH radicals, measurement of OH
concentrations is rather difficult and requires indirect mass spectrometric techniques.
For modelling and data-analysis purposes, it is very useful that UV-B radiation can
be used as a proxy for OH. If measurements of UV radiation are not available, global
radiation (including all wavelengths) can be utilised in many cases, without losing too
much accuracy (Petäjä et al., 2009). However, the intensity of UV-B radiation on the
ground depends highly on the ozone column (the amount of O 3 in a vertical path),
implying that global radiation cannot be used as a proxy for UV-B in regions, where
the ozone column has strong seasonal variation.
Due to its low saturation vapour pressure, the main loss process for sulphuric acid
vapour is condensation onto pre-exisiting aerosol particle surfaces. In addition, nucleation
(if involving sulphuric acid) acts as a sink for sulphuric acid. Thus, the ambient
concentration of sulphuric acid vapour in the atmosphere (C v ) is governed by the equation:
= Q−CS ·C v −J nuc ·n ∗ sa , (22)
where Q is the source rate of H 2 SO 4 (the oxidation rate of SO 2 by OH: Q =
k 16 [SO 2 ][OH]), CS is the condensation sink (see Sect. 2.1.3), J nuc is the nucleation
rate and n ∗ sa is the number of H 2SO 4 molecules in the nucleating cluster.
As a loss process for H 2 SO 4 , the nucleation rate is of minor importance as compared to
condensation, even though nucleation is important with regard to particle formation.
Therefore as a first approximation the balance equation 22 can be rewritten:
dt =Q−CS ·C v (23)
=k 16 [SO 2 ][OH]−CS ·C v . (24)
Thus, the concentration of H 2 SO 4 is affected by the variations in SO 2 and OH concentrationaswell
as thecondensation sink of theaerosol particle population. As explained
above, OH varies according to sunlight (UV radiation). If the variations in SO 2 and
condensation sink are small compared to the variation of the daily cycle of OH, which
often is the case, then the H 2 SO 4 concentration varies approximately according to OH,
and thus according to sunlight.
Figure 6 shows an example of measured H 2 SO 4 concentration, together with the quantities
affecting the its formation: OH radical concentration, solar radiation (mainly
UV-B), SO 2 and water vapour concentration. The overall trend of the H 2 SO 4 concentration
follows roughly that of OH, but has some peaks that can be attributed to the
SO 2 emission peaks fromanthropogenic sources. Notethat Fig. 6 shows only thequantities
affecting the source rate and not the factors influencing the loss rate of H 2 SO 4 ;
the ambient H 2 SO 4 concentration is of course determined by the combined effect of
source and loss processes. Condensation on the background aerosol distribution is the
main loss mechanism for sulphuric acid, and abrupt changes in background aerosol
concentrations can cause rapid changes in the ambient H 2 SO 4 concentration.
Measuring the sulphuric acid concentration in the atmosphere is rather complicated,
and requires mass-spectrometric techniques (Berresheim et al., 2000, see Sect 3.1).
Therefore, based on the balance equation (24), proxies for estimating sulphuric acid
concentation from SO 2 concentration, UV-radiation and CS data have been developed
(Petäjä et al., 2009; Mikkonen et al., 2011). The proxy sulphuric acid concentration
was proven to agree reasonably well with measured H 2 SO 4 concentrations. However,
it should be noted that most of the proxies are constructed based on measurement
data from campaigns in spring and summer time, which may reduce the reliability
of the proxies in predicting the sulphuric acid concentrations during the cold season
(Mikkonen et al., 2011).
In clouds, aqueous reactions of SO 2 in cloud water (inside cloud droplets) is an important
source of sulphuric acid. Other sources for gas-phase sulphuric acid, in addition
to oxidation of SO 2 by OH, may also exist. Just recently, Mauldin III et al. (2012)
proposed a new, possibly important source of atmospheric H 2 SO 4 by reaction of SO 2
with Criegee Intermediates, highly reactive atmospheric biradicals (Welz et al., 2012).
7 x 106 Time (hours)
concentration / Other scaled concentrations
(cm −3 )
OH (cm −3 )
Glob x10 4 (W/m 2 )
UV−B x10 6 (W/m 2 )
x10 7 (ppb)
O x10 6 (%o)
RH x 5x10 4 (%)
4 6 8 10 12 14 16 18 20 22 24
Figure 6: Example of the diurnal profile of sulphuric acid concentration (blue dots),
OH concentration, global and UV-B radiation, SO 2 concentration, water vapour concentration
and relative humidity (RH). The concentrations have been scaled to fit to
the same axis. The data were measured on March 25 th 2003 at the Hyytiälä SMEAR
2.4 Activation of aerosol particles to cloud droplets
Clouds are formed in the Earth’s atmosphere when water vapour in supersaturated
conditions (RH > 100 %) condenses on aerosol particles, thus forming cloud droplets.
In atmospheric temperatures, the homogenous nucleation of water vapour, i.e. formation
of water droplets without a seed aerosol particle, would require a relative humidity
on the order of 400 % (S ≈ 4). These conditions are never met for water vapour in the
Earth’s atmosphere, and therefore all cloud droplets are formed by heterogenous nucleation
and subsequent condensation of water vapour on top of a seed aerosol particle,
which happens at significantly lower saturation ratios. The supersaturated (supersaturation
is defined as SS = S − 1 and expressed typically in %) conditions required
for cloud formation (SS > 0 %) are typically met in the upper boundary layer and in
the free troposphere, where air temperature is low enough to cause a low saturation
vapour pressure and a high enough water saturation ratio. The seed aerosol particles
are called cloud condensation nuclei, abbreviated as CCN.
Activation of an aerosol particle means that water starts to condense irreversibly on
the particle, making it grow into a cloud droplet with size on the order of µm. The
critical diameter is the smallest particle size that gets activated at a certain water
supersaturation. Vice versa, the critical saturation ratio is the saturation required for
a certain particle size and composition in order to start irreversible water condensation
(i.e. activate the particle). The equilibrium between the aerosol particle and water
vapour is described with the Köhler equation:
( 4Mw σ
S eq = a w exp , (25)
where S eq is the water equilibrium saturation ratio, a w is the water activity of the
solution (a w = γ w x w , in which γ w is the activity coefficient and x w is the mole fraction
of water in the solution), M w is the molar mass of water, σ is the surface tension of
the droplet, R is the universal gas constant, T is temperature, ρ is the density of the
solution and d wet is the wet particle diameter. Typically, for the surface tension and
the density the values for water are used (dilute solution).
The Köhler equation combines the curvature effect (the Kelvin effect, Eq. 1), which
increases the equilibium vapour pressure of water on top of the droplet surface, and
the solute effect (the Raoult effect), which decreases the equilibrium vapour pressure
above a solution. As a result, a curve with one maximum is obtained. The Köhler
curve is calculated for a certain dry aerosol particle. The critical saturation ratio S crit
(with a certain dry particle size and composition) corresponds to the maximum of the
Köhler curve: at saturation ratios bigger than S crit , water condenses continuously onto
the particle. At a certain saturation ratio, the corresponding dry particle size can be
obtained by iteratively solving the Köhler-equation: this particle size is the smallest
dry particle that gets activated at the given saturation ratio. This particle size is called
the critical diameter or threshold diameter for cloud droplet activation (Kerminen et
The critical diameter for cloud droplet activationdepends on the water saturation ratio
and on the chemical composition of the aerosol particle. In the atmosphere, the critical
diameters are typically in the range 50–100 nm.
Particle hygroscopicity means its ability to take up water in subsaturated conditions
(S < 1 of RH < 100 %) and it is described by the hygroscopic growth factor:
g a = d wet
where d wet and d dry are diameters of the wet (at certain RH) and dry particle, respectively.
Particle hygroscopic growth factors are measured by Hygroscopic Tandem
Differential Mobility Analyser (HTDMA) for a specific relative humidity (RH).
Another formulation of the Köhler equation was presented by Petters and Kreidenweis
(2007), who expressed the thermodynamic properties of the particle (the solute
effect described by water activity a w ) with the aid of a hygroscopicity parameter κ,
= 1+κ V dry
where V dry is the volume of dry particulate matter and V water is the volume of water in
the solution (V wet = V dry + V water ). With this parametrisation for the water activity,
and a couple of other assumptions, the kappa-Köhler equation can be derived:
S eq (d wet ) =
d 3 wet −d3 (
d 3 wet −d 3 dry (1−κ) exp 4Mw σ
RTρ w d wet
where ρ w is the density of water and σ w is the surface tension of water. Note that particle
density has disappeared from the equation and all the physico-chemical properties
(except the diameter) of the aerosol are captured in the κ-parameter.
The Köhler equation is typically applied at saturation ratios S > 1 necessary for
cloud formation, even though it is valid also for S < 1. The idea of kappa-Köhler
equation is to apply it also for S < 1, thus covering the full range of saturation ratios
from hygroscopic growth (S < 1) to cloud droplet activation (S > 1) (Petters et al.,
2009). By expressing the wet diameter with the aid of the hygroscopic growth factor
(g a = d wet /d dry ), the κ-Köhler equation becomes:
S eq (d dry ) =
g 3 a −1
g 3 a −(1−κ) exp ( A
g a d dry
,A = 4M wσ w
Using HTDMA data on particle hygroscopic growth factors at subsaturated conditions
with a known saturation ratio, the κ-parameter of the aerosol can be determined by
solving it from the kappa-Köhler equation. The higher the value of κ, the more hygroscopic
the aerosol is. Kappa-parametershave been determined in laboratoryconditions
for pure organic aerosol (κ org = 0.1, from α- and β-pinene) and for ammonium sulfate
(κ as = 0.6) as well as in field measurements at several locations (e.g. Gunthe et al.,
2009; Dusek et al., 2010). For purely non-hygroscopic aerosol, such as mineral dust, κ
=0.01–0.08(Koehleretal.,2009). Estimates fortheglobalmeanofκare0.27±0.21for
continental and 0.72±0.24 for marine aerosol (Pringle et al., 2010). The kappa-values
can then be applied to predict the CCN activity of the studied aerosol: to estimate the
critical diameter for cloud droplet activation using the kappa-Köhler equation.
This thesis combines analysis of field measurement data and aerosol dynamical simulations.
This section describes the experimental data, the main data analysis methods
and the aerosol dynamical model used in this study.
3.1 Experimental data
Finland (papers I-III, VI). In paper II also measurement data from the Heidelberg
station in Germany were analyzed.
is located at the Hyytiälä Forestry Field station, about 60 km north-east of the city
of Tampere (http://www.atm.helsinki.fi/SMEAR/). The environment represents a
typical Finnish rural area, with fields and large areas of mixed forest, dominated by
coniferous trees (spruce and pine). The station is affected also by pollution from a
nearby city (Tampere) and industrial sites. The measurement station itself is inside a
roughly 40-year old Scots pine (Pinus Sylvestris L.) forest. The leading idea in setting
to forest and atmosphere: from soil moisture to photosynthetic gas exhange between
vegetation and atmosphere, pollutant trace gases as well as aerosol particle and ion
concentrations. The Hyytiälä SMEAR II station is a unique site for multi-disciplinary
research with high synergetic effects arizing from the possilibity to combine different
sources of data (Hari and Kulmala, 2005).
Particle size distribution measurements
Particle size distributions were measured by a Differential Mobility Particle Sizer
(DMPS) setup. Figure 7 presents the setup operating at the Hyytiälä SMEAR II
station (Aalto et al., 2001) at the present configuration; some details (for example the
charger and the inlet) have changed since the measurements in 2003 reported in paper
The inlet is situated at a height of about 8 m from the ground (until 21.9.2004 the
inlet was at 2 m height) and the measurement devices are located inside a cottage. The
air sample is taken using a TSP-inlet (Total Suspended Particles). Particle sizing is
performed using differential mobility analysers (DMA), which classify aerosol particles
according to their electrical mobility. The sheath flow for the DMA is dried, so that
inside the DMA aerosol is ”dry” at a relative humidity < 30 %. For sizing with DMA
the particles must be charged. This is achieved using a charger with a 14 C betasource
(until 14.10.2008 the charger was 85 Kr), in which the aerosol achieves a charge
equilibrium (for this reason the charger is also called a ”neutralizer”). At a certain
voltage between the plates of a cylindrical DMA, a certain particle size d p ± ∆d p is
C ( )
= 3...50 nm
= 10...1000 nm
* Inversion algorithm:
- d p
- charging probability
- sampling losses
- CPC detection efficiency
Figure 7: A schematic picture of the DMPS (Differential Mobility Particle Sizer) setup
at the Hyytiälä SMEAR II station.
passing through the DMA and this concentration is measured with a condensation
particle counter (CPC). By scanning the voltage of the DMA as a step function, a
size spectrum is obtained. To cover the particle size range 3 nm–1 µm, two parallel
DMA+CPC systems are needed (twin-DMPS): the first one measures the range 3–
50 nm and the second the range 10 nm–1 µm (until 8.12.2004 the upper limit was
500 nm). The voltage scanning is performed in different directions in DMA1 (small
particles) and DMA2 (bigger particles) in order to measure the overlapping part of the
spectra temporally as close as possible. One scan of the whole size distribution takes
about 10 min., defining the time resolution of the twin-DMPS system.
The raw output data from the DMPS is the mobility distribution of the aerosol particles,
which were negatively charged after the 14 C-charger. By applying an inversion
algorithm, the electrical mobilities are converted to particle sizes and the concentration
of neutral aerosol particles (corresponding to the ambient situation before the charger)
is deduced using the particle charging probabilities. The inversion algorithm takes also
into account the estimated particle losses happening in the sampling lines.
The Hyytiälä DMPS system measures particle size distribution with 10 min. time
intervals in 38 channels logarithmically distributed between 3 nm and 1 µm (diameter)
(previously 23 size channels between 3 and 500 nm). The constant RH (about 30 %)
allows for comparison of size distributions despite of big variations in ambient RH.
Sulphuric acid concentration measurements
The gaseous sulphuric acid concentrations were measured with a Chemical Ionisation
during the QUEST II–IV campaigns were performed by a group from Max Planck
Institute (MPI-K Heidelberg) led by Frank Arnold.
The measurement principle of CIMS is to convert sulphuric acid molecules (H 2 SO 4 )
to ions by a chemical reaction, after which the concentration of the product ions can
be measured by a mass spectrometer (Fiedler et al., 2005; Aufmhoff et al., 2011).
The instrument consists of an ion source (NO − 3 (HNO 3) n -ions), a flow reactor and the
quadrupole mass spectrometer, as well as a H 2 SO 4 source for the calibration of the
instrument. In the flow reactor, a fast ion-molecule reaction between NO − 3(HNO 3 ) n -
ion and H 2 SO 4 happens:
NO − 3 (HNO 3 ) n +H 2 SO 4 → HSO − 3(HNO 3 ) m +(n−m)HNO 3 .
The concentrations of reagent (NO − 3(HNO 3 ) n ) and product ions (HSO − 3(HNO 3 ) m )
are measured with the quadrupole MS. The concentration of H 2 SO 4 can then be inferred
from the ratio of these concentrations when the reaction rate constant is known
(Berresheim et al., 2000). The detection limit for sulphuric acid was 1·10 5 cm −3 and
the relative measurement error 30 %. The time resolution of the spectrometer was less
than 1 s, but the data was averaged over 60 s in order to reduce statistical error.
The CIMS instrument has also been used to measure other atmospheric trace gases,
such as volatile organic compounds (Sellegri et al., 2005) and OH (Berresheim et al.,
2000; Petäjä et al., 2009; Aufmhoff et al., 2011).
Cloud condensation nuclei and hygroscopicity measurements
The cloud condensation nuclei concentrations were measured at ground level at the
SMEAR II station by a CCN-counter (CCNC, model DOC-0086 by Droplet Measurement
Technologies). The CCN-counter mimics the conditions inside a cloud and measures
the number of particles that are activated for cloud droplets at a certain water
to the total particle concentration, the activated fraction can be determined; by comparing
the number of activated particles with the particle size distribution, an estimate
of the critical diameter for cloud droplet activation can be obtained. The instrument
operates at supersaturations from 0.07 % to 3 %, thus capturing the typical conditions
prevailing in cloud formation. At the SMEAR II station the CCNC instrument
operates at water supersaturations of 0.1–1.0 %.
( T > T > T )
3 2 1
( T )
A, sat A
T , p ( T )
diffusion of heat
and water vapour
( T )
Figure 8: A schematic picture of the Cloud Condensation Nucleus Counter (CCNC).
The operation of the CCN-counter is based on the principle that diffusion of heat in
air is slower than diffusion of water vapor (Roberts and Nenes, 2005; CCNC manual).
Figure 8 presents a schematic of the CCN-counter. An aerosol sample is led through a
cylindrical flow chamber, which has wetted walls for providing a constant water vapour
source and a constant, increasing temperature gradient over the cylinder height. The
water vapour(saturationconcentration prevailing above thewetted walls) andheat diffusefromtheoutershell
inwards, tothecenter ofthecylinder. Because watermolecules
diffuse more quickly than heat (due tothe smaller size ofaH 2 O molecule in comparison
to air molecules N 2 and O 2 ), the vapour concentration and heat (temperature) at the
centerline (point C) originate from different locations on the wall (points A and B): at
point C there is a concentration p sat (T B ) of water vapour at a temperature of T A . Because
T A < T B , the vapour is supersaturated at C: S = p sat (T B )/p sat (T A ) > 1. Due to
the constant temperature gradient, in the centerline of the cylinder there is a constant
supersaturation prevaling (actually S > 1 almost everywhere inside the cylinder).
The supersaturation at the centerline of the flow tube, where the aerosol sample is
flowing, depends on the temperature gradient between bottom and top of the cylinder,
flow rate and pressure. While the flow rate and pressure are kept constants, the
operating supersaturation is chosen by adjusting the temperatures T 1 , T 2 and T 3 . At
a given supersaturation, particles bigger than the critical diameter activate (i.e. water
starts to condense on them irreversibly) and continue to grow fast as they travel in
the centerline of the flow tube (to about to some µm in diameter). The concentration
of activated cloud droplets is then counted by an optical particle counter (OPC). The
OPC detects particles of size 0.75–10 µm and allows also a rough sizing of the droplets.
In this work, the droplet size detection possibility of the CCNC was not utilized.
Mobility Analyser (HTDMA) (Ehn et al., 2007). The principle of the instrument is
to first select a dry aerosol particle size with a DMA, then lead the sample through a
humidifier with a specified RH (RH < 100 %), and after that measure the humidified
size distribution. From the humidified distribution (which may be uni- or multimodal
depending onthe mixing state of the aerosol) the growth factor distribution is obtained
by dividing it by the original dry diameter (see Eq. 26).
Meteorological and gas data
In addition to the data described above, accompanying data of meteororological
variables (T, p, RH) and common trace gases (H 2 O, SO 2 etc.) were utilized
in the data analysis (for the measurement methods see SMEAR webpage
3.2 The calculation of particle formation rate
The particle formation rate J dp is defined as the number of particles of diameter d p
formed per cm 3 per second. In atmospheric particle formation studies, the common
terminology is as follows:
- ”the nucleation rate” is the formation rate of the smallest stable clusters. According
to current knowledge, the size of the nucleated clusters is 1–2 nm (Kulmala et al.,
2007). The nucleation rate is marked as J nuc , J 1 or J 2 (subscript referring to the size
in nm). The unit is particles/(cm 3 s) = cm −3 s −1 .
- ”the particle formation rate” refers to the formation rate of particles at some other
size than the nucleation size. Often the size of interest is set by the lower detection
limit of the measurement instrument, e.g. 3 nm (in diameter) for the conventional
aerosol instruments (CPC, DMPS and SMPS). The rate is marked as J dp , for example
J 3 , and the unit is cm −3 s −1 . Sometimes also the term ”apparent particle formation
rate” is used.
This distinction of the nucleation rate and the particle formation rate was first suggested
by McMurry and Friedlander (1979) and has become a common convention in
3.2.1 Particle formation rate at 3 nm
Let us consider first a continuous particle size distribution at the diameter d p = 3 nm.
We can write for the number concentration at 3 nm:
∣ = dN ∣ ∣∣3 dd p
∣ = n(d p ) ∣ 3 dd p dt 3 3
×GR 3 ≡ J 3 , (30)
where n(d p ) ∣ ∣
= dN/dd p
∣3 is the size distribution function at d p = 3 nm and GR 3 =
dd p /dt is the diameter growth rate of 3 nm sized particles. This is the mathematical
definition of the particle formation rate at 3 nm, J 3 (provided that self-coagulation is
not significant). In words, J 3 means the flux of particle concentration on the diameter
axis at size d p = 3 nm (see Fig. 9). In principle, if we know the size distribution and
growth rate accurately at 3 nm, one could apply directly Eq. 30 to calculate J 3 , or in
practice with an approximated expression (Weber et al., 1996):
J 3 = n(d p ) ∣ ∣
GR 3 , (31)
where ∆N is the particle number concentration at a narrow size range ∆d p around
d p = 3 nm. This expression has been used by some researchers to estimate J 3 from
PHA (Pulse Height Analysis method) and nano-SMPS (Scanning Mobility Particle
Sizer, similar to DMPS) data, with particle size ranges ∆d p = 3–4 nm (PHA) and ∆d p
= 3–6 nm (nano-SMPS) (Weber et al., 1997; Kuang et al., 2008).
We adopt a sligtly different method for the calculation of the particle formation rate,
in which the particle size distribution is explicitly considered as a discrete distribution
(Kulmala et al., 2001a). This corresponds to the real case of aerosol measurements,
where the particle size distribution is measured as discrete channels. For one size bin
at diameter d p,i we can write the balance equation for the number concentration N i :
= J i −J i+1 −Coag. loss, (32)
where J i is the flux into the size bin (= formation rate of particles at the lower limit of
the bin), J i+1 is the flux out of the size bin at the upper limit of the bin, and Coag. loss
is the loss rate of particles due to coagulation with other (larger) particles of the size
distribution. The quantities are depicted in Figure 9. This balance equation can be
derived from the general dynamic equation (Eq. 4) by integrating it over the particle
diameter range ∆d p,i (paper V).
Applying Eq. 32 for the particle size range 3–6 nm and using the definition of particle
formation rate (J dp , Eq. 30) we get:
Figure 9: A schematic picture of the quantities affecting the particle concentration N i
in a size bin d i ...d i+1 .
= J 3 −J 6 −Coag. loss
≈ n 3 GR 3 −n 6 GR 6 −CoagS dp=4nmN 3−6 , (34)
where the coagulation loss has been expressed with the aid of the coagulation sink.
To simplify the calculation, the coagulation loss for 3–6 nm particles is approximated
by the coagulation loss of 4 nm sized particles having the concentration N 3−6 (4 nm
is close to the geometric mean of 3 and 6 nm). The size range 3–6 nm was chosen,
because it is small enough to be considered as freshly nucleated, but large enough to
achieve relatively good statistics for the number concentration. In addition, the same
size range has been used in earlier studies of atmospheric nucleation (Weber et al.,
By solving Eq. 34 for J 3 we obtain:
J 3 = dN 3−6
+n 6 GR 6 +CoagS dp=4nmN 3−6 . (35)
Calculating the size distribution function from N 3−6 as n 6 = ∆N 3−6 /∆d p , using the
growth rate determined from the DMPS data (for size range 3–10 nm) and approximating
differentials with finite differences, we get:
J 3 = ∆N 3−6
(6−3) nm GR DMPS +CoagS dp=4nmN 3−6 . (36)
This is the equation which is used to calculate the formation rate of 3 nm particles
from the size distribution data measured with DMPS.
3.2.2 Estimation of the nucleation rate from the apparent particle formation
After nucleation, the newly formed particles grow by condensation and are scavenged
by coagulation with the pre-existing particle size distribution. In the absence of coagulation
(and other removal mechanisms) J 3 would equal the nucleation rate J nuc
(J 3 (t + ∆t) = J nuc (t)), after a time delay ∆t associated with the growth time from
nucleated size (d nuc ) to 3 nm. With coagulation scavenging, which acts as a sink for
particles during the growth from d nuc to 3 nm, the particle formation rate at some
other diameter is always smaller than the real nucleation rate: J 3 (t+∆t) < J nuc (t).
Inmeasurements, thetypical lower detectionlimit (e.g. DMPSandSMPSinstruments)
for particle size is d p = 3–10 nm, even though recent advances in aerosol instrumentation
have pushed the detection limit down to 1–2 nm (NAIS, PSM; Asmi et al., 2009;
Sipilä et al., 2009; Vanhanen et al., 2011). Anyhow, a vast majority of aerosol measurements
are still done with a lower detection limit of 3 nm. For nucleation studies, it
would be useful to be able to estimate the real nucleation rate at 1 nm or 1.5 nm from
the observed apparent particle formation rate at some greater diameter, say 3 nm.
The original Kerminen-Kulmala formulation
Kerminen and Kulmala (2002) presented a formula connecting the apparent particle
formation rate J dp at a diameter d p with the nucleation rate J nuc at diameter d nuc :
J dp (t+∆t) = J nuc (t)exp
(γ CS′ 1
− 1 ))
GR d p d nuc
where GR is the particle growth rate (in units nm/h)) and nucleated size d nuc and
particle size d p are expressed in meters (m). CS ′ (units m −2 ) is directy proportional
to the condensation sink (CS):
CS ′ = 1 2
β m,i d p,i N i = CS
where D v is the diffusion coefficient of the condensing vapour (assumed to be sulphuric
acid). γ in Eq. 37 is a fitting parameter with an approximate value of 0.23 nm 2 m 2
h −1 .
Equation 37 takes into account the competition between coagulational scavenging
(through the term CS ′ ) and condensational growth (through the term GR) during
growth from the nucleated size d nuc to a size d p . The exponential represents the probability
that a nucleated cluster of size d nuc , subject to coagulation and condensational
growth, will survive to the size d p . The time delay ∆t arises from the the growth time
from d nuc to d p : ∆t = (d p −d nuc )/GR.
The Kerminen-Kulmala equation (referred to as the K-K equation) was derived under
three main assumptions (Kerminen and Kulmala, 2002):
(i) coagulation to background aerosol is the only sink for nucleated particles, i.e.
self-coagulation and dry deposition are neglected. Neglecting self-coagulation is
justified if concentations are below 10 5 –10 6 cm −3 .
(ii) the particle growth rate is constant during growth from d nuc to d p .
(iii) background aerosol (i.e. CS’) stays constant during the growth from d nuc to d p .
The K-K equation was derived analytically, but it contains a fitting parameter γ,
which arises from expressing the coagulational scavenging (the coagulation sink) in
terms of the condensation sink. The reason behind this is that at small particle sizes,
approaching the molecular size, coagulation can be thought of as condensation of nmsized
particles onto the background distribution. Also, CS is often the quantity that
is calculated from measured particle size distributions, and is more straightforvard to
calculate than CoagS.
The Brownian coagulation coefficient of d p -sized particles is proportional to d −κ
p , where
the exponent κ is in the range 1.5–2 (Kerminen and Kulmala, 2002; Seinfeld and
Pandis, 2006). Kerminen and Kulmala assumed κ = 2, and thus the coagulation sink
of d p -sized particles can be expressed as:
CoagS dp = γ ′ ·CS ′ (
= γ ·CS ′ ( 1
The proportionality factors γ ′ and γ connect CoagS(d p ) to CS ′ . Based on fittings to
data from aerosol dynamical simulations, Kerminen and Kulmala (2002) presented a
parametrisation for γ which depends weakly on many factors such as temperature and
nucleated particle density. However, usually an approximate value of 0.23 nm 2 m 2 h −1
is accurate enough for atmospheric particle formation studies.
In connection with aerosol measurements, the K-K equation is often used in the reverse
direction, i.e. to estimate the nucleation rate fromthe observed particle formationrate:
J nuc (t) = J dp (t+∆t)exp
(−γ CS′ 1
− 1 ))
GR d p d nuc
Usually the equation is used at the lower detection limit of particle size distribution
measurements, i.e. at d p = 3 nm, and with nucleation size in the range 1–2 nm.
The Kerminen-Kulmala equation has proved to be very useful in testing and developing
nucleation theories (e.g. papers I and II). With this equation we can obtain
quite reliable estimates of the actual nucleation rates, when accurate measurements of
nucleation rate at the real nucleation size (1–2 nm) are missing. Another important
use of the K-K equation is in large scale atmospheric models, where it (in the form of
Eq. 37) can be used to transfer nucleation rates to particle formation rates e.g. at 3
or 10 nm, without the need to model all the initial steps of particle growth in detail.
The Kerminen-Kulmala equation corresponds to a similar formula presented by Mc-
Murry and Friedlander (1979). However, the Kerminen-Kulmala equation has become
more popular, most probably because it is easier to apply and uses two main quantities
that are determined in new particle formation event studies, namely GR and CS. In
their paper, McMurry et al. (2005) present a rigorous examination on the connections
between these two similar methods to estimate nucleation rates from the apparent
particle formation rate.
The revised form of the Kerminen-Kulmala equation
Afterwards, Lehtinen et al. (2007) have presented a revision for the Kerminen-Kulmala
equation. In their formulation, two improvements were made: the coagulation scavenging
is calculated explicitly from the coagulation sink (not through the condensation
sink) and a more accurate expression for coagulation sink is used. Instead of assuming
the coagulation sink to be proportional to the square of the particle diameter (Eq. 39),
the exponent is kept as a free parameter:
CoagS(d p ) = CoagS(d nuc )·
where CoagS(d nuc ) is the coagulation sink of nucleated particles and m = −κ. By
solving this, an equation for the exponent m is obtained:
m = log[CoagS(d p)/CoagS(d nuc )]
log[d p /d nuc ]
By this equation the value of exponent m (typically in the range [−2,−1.5]) can be
calculated directly from the particle size distributions. At the Hyytiälä SMEAR II
station, m varies in the range [−1.75,−1.5] with a mean value −1.7 (Lehtinen et al.,
The main improvement of this approach is that we get rid of the fitting parameter
γ, which in the K-K formula was adjusted based on modelling results. With the new
expression for the CoagS (Eq. 41), a new equation for the apparent particle formation
rate was obtained:
CoagS(d nuc )
J dp (t+∆t) = J dnuc (t)exp −γ d nuc ,
where γ =
[ ( ) ] m+1
m+1 d nuc
Note that here the parameter γ is a dimensionless parameter, and different from the
one in the original form of the K-K-equation. To get the units correct in this equation,
the CoagS has to be expressed in units h −1 , if the GR is in nm/h.
There are a couple of advantages in the revised version of the K-K equation. First, it
is conceptually more clear to use directly the coagulation sink instead of condensation
sink for calculating the coagulational scavenging. Also, the dependence of the condensation
sink on the diffusion properties of the condensing vapour is avoided. Second,
the coagulation scavenging is calculated more accurately. Third, the varying ambient
conditions are more easily taken into account, as the parameter m can be calculated
explicitly from the particle size distributions.
The revised version of the K-K equation (Eq. 43) is applied as follows. First, the
proper value of m is calculated from experimental particle size distribution data, to
represent the conditions of the studied case. The parameter m can be determined for
theaverage conditions of the station, or even separately for each new particle formation
event. Then the particle formation rate is evaluated using Eq. 43.
In addition to the modification by Lehtinen et al. (2007), a few other improvements
have been presented to the original K-K equation. Kerminen et al. (2004) presented a
formulation which accounts for, in addition to sulphuric acid, an organic vapour contribution
to the particle growth, and allows for a time-dependent growth rate. Anttila
et al. (2010) included in their parameterisation the effects of self-coagulation of freshly
nucleated particles. However, in most cases of atmospheric particle formation (when
the nucleation rates are not too high and the growth rate is not varying fast), the original
formulation by Kerminen and Kulmala (2002) or Lehtinen et al. (2007) is accurate
In the articles included in this thesis, the original formulation of the K-K equation
(Eqs. 37 and 40) was used, except in paper III, where the new, revised formula by
Lehtinen et al. (2007, Eq. 43) was applied. In future studies, the use of the revised
formula is recommended.
3.3 Evaluation of the calculation method of J 3
Equation 36 has been widely used for estimating the new particle formation rate from
measured particle size distribution data. In paper V we studied the accuracy of this
calculation method to predict the actual particle formation rate at 3 nm. The study
wasbasedonsimulationsmadewiththeUniversity ofHelsinki Multicomponent Aerosol
model (UHMA; see Section 3.4 for description of the model). Using simulated data,
the exact particle formation rate at 3 nm (J 3 ) as well as other model conditions are
known, and can be compared with the estimate given by approximate equation (36).
For the evaluation study, a new particle formation event, similar to the observed new
particle formation events, was produced with the UHMA model (Fig. 10). The nucleation
mechanism was activation nucleation (see Sect. 4.2) at a diameter of 1.5 nm,
and particle growth was caused by sulphuric acid and a non-volatile organic vapour.
Both vapours had a sinusoidal-like diurnal profile, while the concentration of organic
vapour was significantly higher than that of H 2 SO 4 , so that particle growth was caused
mostly by the organic vapour. The background particle distribution corresponded to
a typical case in Hyytiälä.
From the simulated data, the particle formation rate at 3 nm was calculated by Eq.
31 (corresponding to the Eq. 3 in paper V):
J 3 = ∆N
GR 3 , (44)
where ∆N/∆d p | 3 is the size distribution function and GR 3 is the growth rate at d p
= 3 nm. Let us denote this formation rate as ”J 3 , exact”. This formation rate is
called ”exact”, since we get the values of particle size distribution ∆N/∆d p and the
growth rate GR 3 directly from the simulated data, and the formula (Eq. 31 or 44) does
not contain any approximations despite the calculation of n 3 from the discrete model
data. In the simulated case we used 60 size sections (as compared to 23 size sections
in the measured data), so discretization will have only a minor effect on the results.
Consequently, J 3 calculated by Eq. 44 can be considered to represent the actual J 3
For evaluation of the validity of the J 3 calculation methods, Eq. 36 was applied to
the modelled event in the same way as for a measured particle formation event. The
∆N 3−6 /∆t, N 3−6 and CoagS dp=4nm were obtained directly from the simulated discrete
particle size distribution. The growth rate was calculated in two ways: i) directly from
the condensation rate of vapours, calculated as an average for particle sizes 3–7 nm, or
ii) by estimating a constant GR from the time evolution of the nucleation mode peak
diameter between 3–7 nm (GR = ∆d p /∆t). The first method (i) is applicable only
withthesimulated dataandgivesatime-dependent (but size-averaged) GR. Thelatter
method (ii, denoted as ”constant GR”) is the way the growth rate is determined from
measured new particle size distribution data (Hirsikko et al., 2005). Thus Eq. 36 with
the ”constant GR”-growth rate corresponds to the measurement case for calculating
J 3 .
The investigation showed that Eq. 36 (corresponds to Eq. 5 in paper V) gives a fairly
good estimate for new particle formation rate J 3 (see Fig. 10). The equation tends to
overestimate the particle formation rate J 3 , as compared to the exact values given by
Eq. 44, with an error of 10–20 %. Surprisingly, the J 3 estimation is better with the
Formation rate [cm −3 s −1 ]
Eq. 5 (constant GR)
6 8 10 12 14 16 18
Figure 10: Simulated new particle formation event (left) and comparison of different
methods to calculate the particle formation rate J 3 during this event (right) (same as
Figs. 2 and 3 in paper V). Note that the legend refers to the equations of paper V.
”constant GR” growth rate, i.e the method used in analyses of measured data, than
with the more exact, time-dependent GR calculated from the simulation. This effect
is most probably caused by a fortuituos error cancellation.
The sensitivity studies presented in paper V indicated that most of the error in J 3
calculation (Eq. 36) can be attributed to coagulation and its various effects. Between 3
and6nmparticlesexperience significant coagulationscavenging tobackground aerosol,
with the coagulation rate decreasing as particles grow larger (from 3 to 6 nm). The
coagulational scavenging term CoagS 4 × N 3−6 is only a rough approximation to the
coagulation rate of 3–6 nm particles. The other main error source is the calculation of
J 6 : J 6 = n 6 GR 3−7 (Eq. 31), where the size distribution function was approximated as
n 6 = N 3−6 /(6−3)nm. Due to decreasing coagulation rates, more particles at 3 nm are
removed by coagulation than at 6 nm, and thus the mean number concentration in the
size range 3–6 nm, N 3−6 , is not the best estimate for n 6 close to upper diameter 6 nm.
A better choice would be to estimate n 6 from a size range closer to 6 nm, e.g. 5–7 nm:
n 6 ≈ N 5−7 /(7−5)nm.
Applying themoreaccuratecalculation forn 6 improved theestimate ofJ 3 significantly;
the error in J 3 was reduced to only 6 %.
In this study, the effect of self-coagulation was neglegted, but the effect should be small
at these concentrations (significant only at very high number concentrations).
With this modification to the n 6 estimation, a new formula for calculating J 3 was
proposed (corresponds to Eq. 6 in paper V):
J 3 = ∆N 3−6
+ N 5−7
(7−5)nm GR 3−7 +CoagS dp=4nmN 3−6 . (45)
Because this improvement is straightforward to implement, in paper V we recommend
this new form of J 3 equation to be used in the analyses of experimental particle
It is clear that also the growth rate GR 3−7 , calculated from the time evolution of the
nucleation mode, has inaccuracies (Leppä et al., 2011), but those errors are hard to
quantify andso far no other reasonable way to estimate growth rates exists. Simulation
results showed that the J 3 calculation was quite sensitive to the value of the growth
This study (paper V) was to our knowledge the first attempt to estimate the validity
of the particle formation rate calculations, which have been perfomed for a wide range
of measurement data from different locations. It gave confidence that the method
used to estimate J 3 gives generally fairly good results, and the magnitude of error is
acceptable. However, the study was based on only one type of new particle formation
event, although several sensitivity tests on the simulation conditions were performed.
new particle formation events would be needed in order to find out if these results
are statistically valid, and what is the uncertainty in the calculation of J 3 for larger
3.4 University of Helsinki Multicomponent Aerosol model
Aerosol dynamical simulations were carried out in order to gain insight into the processes
behind atmospheric particle formation (papers III–V). The advantage of an
aerosol dynamical model is that we can track the whole process of atmospheric particle
formation from nucleation size at 1–2 nm up to 500 nm under controlled conditions.
The simulations were performed using the University of Helsinki Multicomponent
Aerosol model (UHMA), which has been developed at the University of Helsinki by
Korhonen et al. (2004) and designed specifically for studies of new particle formation.
UHMA is a box-model to simulate the dynamics of the aerosol population in a uniform
”box” of air, without any advection or turbulent transport fluxes. It calculates the evolution
of the aerosol size distribution under all the basic aerosol dynamical processes
for clear-sky conditions: nucleation, condensation, coagulation and dry deposition.
The two main approaches in atmospheric modelling are the Eulerian and Lagrangian
frameworks. In the Eulerian framework, a situation at stationary observer is modelled,
whereas in the Lagrangian framework, a situation for an observer moving with the
air flow is considered. In principle, as UHMA does not include advective mass transfer,
it represents a Lagrangian modelling framework. The measurements e.g. at the
Hyytiälä SMEAR II station, however, are done at a stationary point i.e. in an Eulerian
perspective. The results from a Lagrangian box-model can be compared to measurements
at a stationary station, provided that air flow at the station is from the same
direction for a sufficiently long time, and no strong horisontal transport occurs (calm
conditions). In that case the station is observing the same and rather homogenous air
mass. This condition is often fulfilled for the class I events (Dal Maso et al., 2005; an
example shown in Fig. 2). In the steady conditions of one air mass, the observed new
particle formation behaves smoothly, having a steady growth without abrupt changes
in the size distribution.
Figure11: ThestructureoftheUHMA(University ofHelsinki Multicomponent Aerosol
model). The model is a 1-dimensional box-model designed for particle formation studies.
ThebasicstructureoftheUHMAmodelispresentedinFig. 11. Asaninput, themodel
takestheinitialparticlesizedistributionandcomposition. Inaddition, thecondensable
The model then calculates the dynamics of the aerosol population, subject to the four
aerosol dynamical processes, according to the General Dynamic Equation (Eq. 4). In
the basic version of UHMA, the integration of differential equations is performed with
the simple, 1 st order Euler-forward method. At chosen time intervals, e.g. 10 min., the
model gives as an output the current particle size and composition distribution as well
as the concentrations of condensable gases.
UHMA is a sectional model, meaning that the size distribution is divided into sections
uniformly distributed on a logarithmic particle diameter axis. The number of sections
can be chosen freely according to the accuracy needed in the study; typically 40–60
sections between 1–500 nm are used. Particles are assumed to be totally internally
mixed within a size section, i.e. all particles in a size bin have the same composition.
The particles are composed of the following ”substances”: sulphuric acid, 1–3 organic
compounds, a possible insoluble core, ammonia and water.
Condensation is calculated using the transition-regime theory of Fuchs and Sutugin
(1971) (also in Seinfeld and Pandis, 2006), with the modification by Lehtinen and
Kulmala (2003) for the molecular regime condensation flux. For condensation calculations,
UHMA applies a hybrid-sectional method, in which the particle is divided into
a ”core particle” part including sulphuric acid, organic compound(s) and possible nonsoluble
core-particle, and a ”non-core part” including water and ammonia. For the
”core” part the condensation (or evaporation) flux and the resulting diameter increase
(or decrease) is calculated explicitly from the condensation equations, whereas water
and ammonia uptake are calculated through an equiliblium parameterisation, which
depends on relative humidity, ammonia concentration, particle size and composition
(Napari et al., 2006). One of the condensing organic compounds can be set to be
a ”nano-Köhler”-compound, meaning that its condensation follows the nano-Köhlermechanism
proposed by Kulmala et al. (2004a) (see Sect 2.1.1). If more than one
condensable organic compounds are used, the rest are assumed to be water-insoluble
and follow the normal Kelvin effect.
Coagulation is calculated according to the conventional equations by Fuchs (1964,
also in Seinfeld and Pandis, 2006). Dry deposition follows a parameterisation for
Hyytiälä conditions by Rannik et al. (2003). For nucleation, several different parameterisations
can be used: binary, ternary, activation and kinetic nucleation mechanism.
To update the model for this study, I added the subroutines for activation and kinetic
nucleation mechanisms (Sect. 4.2, Eqs. 46 and 47) as well as a subroutine for sulphuric
acid production rate. The sulphuric acid production rate is calculated as a chemical
reaction rate of SO 2 and OH, while for OH a sinusoidal profile dependent on the zenith
angle of the sun was assumed, correspoding to cloudless conditions.
In this study, the following model set-up was applied (for the base case): Particles
consist of sulphuric acid, water, ammonia and one nano-Köhler-organic compound.
The properties of the organic compound were chosen to correspond to a possible VOC
oxidation product with a saturation vapour concentration c sat ≤ 10 6 cm −3 (c sat corresponds
to saturation vapour pressure via ideal gas law) (Kulmala et al., 1998b, 2001b).
The sulphuric acid saturation concentration is assumed to be zero, i.e. it condenses
with the maximum flux. For the activation and kinetic coefficients the mean values
determined for the QUEST II campaign (Hyytiälä) were used, namely A = 1 × 10 −6
s −1 and K = 5×10 −13 cm −3 s −1 (paper I).
The UHMA model (and its modified versions) has been applied widely in studies of
atmospheric aerosols and particle formation: in combination with a chemistry model
for new particle formation studies (Grini et al., 2005); in a pseudo-Lagrangian way for
simulating aerosol transformation during continental transport, with a simple treatment
for boundary layer entrainment/detrainment (Komppula et al., 2006; Tunved
et al., 2006b); in studies of iodine oxide induced nucleation in coastal, marine environment
(Vuollekoski et al., 2009; Ehn et al., 2010); for investigating sea salt aerosol
and its effect on marine aerosol and cloud droplet number concentrations (Mårtensson
et al., 2010); and for studying cloud processing and CCN activation (Korhonen et al.,
2005). Leppä et al. (2009) have developed a model version including atmospheric
ions and charged particles. In addition, UHMA has been incorporated as part of a
1-dimensional columnar model MALTE (Boy et al., 2006; Lauros et al., 2011).
4 Connection between sulphuric acid and new particle
As described in previous sections, sulphuric acid is the key compound in atmospheric
nucleation. In addition to nucleation, sulphuric acid participates in the condensational
growth of particles. Due to its extremely low saturation vapour pressure, sulphuric
acid starts to condense already on the smallest, freshly nucleated particles.
The main part of this thesis studies the correlation of new particle formation with
sulphuric acid concentration. This correlation was studied both by analyzing field
measurement data (papers I–III) and by conducting aerosol dynamical simulations
(paper IV). This chapter describes the results published in papers I–IV.
4.1 General correlation of sulphuric acid and new particle formation
in the field data
An important background to this study are the measurements by Weber et al. (1995,
1996, 1997), which reported concurrent measurements of sulphuric acid and freshly
nucleated particle concentrations in the 3–4 nm size range at a marine site (Mauna
Loa) and a continental site (Idaho Hill) in USA. They observed the formation rate
of 3 nm particles to be correlated with the ambient sulphuric acid concentration to
the power between 1–2, a much smaller power than predicted by classical nucleation
theory. Their measurements indicated, that nucleation would be collision controlled
(McMurry and Friedlander, 1979), but with a rate about three orders of magnitude
smaller than the kinetic collision frequency of the hydrated H 2 SO 4 molecules. Weber
et al. (1997) speculated that this would be caused by ammonia needed to stabilize the
H 2 SO 4 -H 2 O clusters.
After the studies by Weber et al., few research efforts were devoted to investigating
the correlation of particle formation with H 2 SO 4 , probably due to the lack, at that
time, of mass spectrometric instruments needed for the measurement of sulphuric acid.
The correlation between sulphuric acid and particle formation rate was ”rediscovered”
after the measurements of the QUEST II campaign in Hyytiälä in 2003, where the
sulphuric acid concentration was measured continuously with a good time resolution
using a chemical ionisation mass spectrometer (CIMS) (Fiedler et al., 2005; Kulmala
et al., 2006). The QUEST II campaign was the first field campaign in Hyytiälä with
continuous sulphuric acid concentration measurements.
The correlation studies presented in this thesis started from the observation, that on
some days the number concentration of freshly nucleated particles (3–6 nm in diameter)
follows nicely the sulphuric acid concentration after some time delay (Fig. 12).
The striking similarity between these quantities strongly suggests that sulphuric acid
participates in nucleation. The time delay ∆t arises from the time needed for growth
from the nucleation size ( 1–2 nm; in papers I–II nucleation at 1 nm was assumed)
to the detection limit 3 nm of the DMPS.
10 4 Day of year
Concentration (1/cm 3 )
∆ t = 1.4 h
84 84.2 84.4 84.6 84.8 85
Figure 12: The number concentration of 3–6 nm particles and the concentration of gas
phase sulphuric acid on 25 th March (day 84), 2003, at the Hyytiälä SMEAR II station,
an example of a pure ”activation day” with linear correlation between sulphuric acid
andN 3−6 . Thenumberconcentrationoffreshlynucleatedparticlesfollowsthesulphuric
acid concentration after a time delay of approximately 1.4 hours.
The correlations between new particle formation and gas-phase sulphuric acid concentration
were studied in detail in papers I and II. The study was based on analysis
of field data, measured during three campaigns: QUEST II campaign in 2003 in
Hyytiälä, Finland (paper I), QUEST III campaign in 2004 in Heidelberg, Germany
(paper II), and BACCI/QUEST IV campaign in 2005 in Hyytiälä (paper II). These
data sets offered good material to investigate the connection between new particle formation
(abbreviated hereafter as NPF) and sulphuric acid in different environments,
Hyytiälä representing a ruralsite inboreal forest environment andHeidelberg a slightly
more polluted site in Central Europe.
We studied the correlation with sulphuric acid separately for the number concentration
of 3–6 nm particles (N 3−6 , obtained from the lowest four channels of the DMPS
measurements), for the formation rate of 3 nm particles (J 3 , calculated from DMPS
data by Eq. 36) and for the formation rate of 1 nm particles (J 1 i.e. the nucleation
rate, calculated by Eq. 40). In all data sets, both the number concentration N 3−6
and the particle formation rates (J 3 and J 1 ) were observed to correlate with sulphuric
acid concentration to the power of 1–2 (see Fig. 13). The correlations were very similar
in all three data sets, suggesting that the nucleation mechanism is similar in both
environments, Hyytiälä and Heidelberg.
To examine the correlations in more detail, we determined for each day the exponent
maximizing the correlation coefficient, separately for the three relationships: N 3−6 ∼
[H 2 SO 4 ] n , J 3 ∼ [H 2 SO 4 ] n andJ 1 ∼ [H 2 SO 4 ] n . These”best-fit”exponentsarecalledhere
the correlation exponents and labelled asn N3−6 , n J3 and n J1 . In all three data sets there
QUEST II Hyytiälä
QUEST III Heidelberg
QUEST IV Hyytiälä
(cm −3 s −1 )
(cm −3 s −1 )
QUEST II Hyytiälä
QUEST III Heidelberg
QUEST IV Hyytiälä
10 4 10 5 10 6 10 7
(cm −3 ) (delayed by ∆t)
10 4 10 5 10 6 10 7
(cm −3 )
Figure 13: Formation rate of 3 nm particles (J 3 ) (left) and 1 nm particles (J 1 ) (right)
versus sulphuric acid concentration during the three QUEST campaigns in Hyytiälä,
Finland, and in Heidelberg, Germany. The straight lines correspond to the linear and
squaredrelationship between J dp and[H 2 SO 4 ](withslopes1and2onlogarithmicaxis).
were pure exponent n = 1 days (linear correlation with [H 2 SO 4 ]) and pure exponent
n = 2 days (squared correlation with [H 2 SO 4 ]), as well as variants between n = 1–2
(Table 1). The correlation exponents could be different for N 3−6 , J 3 andJ 1 , typically in
the order that n N3−6 ≤ n J3 and n N3−6 ≤ n J1 . Based on simple theoretical calculations,
the change in the correlation exponent was attributed to sulphuric acid participating
in the growth of nucleated clusters (paper II). This conclusion was supported also by
the results from aerosol dynamical simulations presented in paper IV.
Thetimedelaybetweentherisein[H 2 SO 4 ]andN 3−6 canbeusedtoestimatethegrowth
rate of nucleated clusters from the nucleation size at 1 nm to 3 nm: GR 1−3 = 2nm/∆t
(Fiedler et al., 2005). The mean values for the initial particle growth rates were 1.2–3
nm/h in Hyytiälä and 1.3 nm/h in Heidelberg.
The strong correlation of particle formation rates and number concentration with the
H 2 SO 4 concentration implies that sulphuric acid is participating in nucleation and/or
growth of freshly nucleated particles. However, the correlation analysis does not give
ultimate proof that sulphuric acid is the nucleating compound. In principle, there
are three possibilities which could produce the observed correlation between NPF and
(i) sulphuric acid participates only in nucleation (= formation of stable clusters
around 1–1.5 nm);
(ii) sulphuric acid participates in initial particle growth, but nucleation happens by
other substances (e.g. organic compounds);
(iii) sulphuric acid participates both in nucleation and initial particle growth.
Table 1: The exponents of the correlation N 3−6 ∼[H 2 SO 4 ] n (R is the mean correlation
coefficient) and the median values of the nucleation coefficients A and K for the
QUEST II–QUEST IV campaigns (paper II).
QUEST II QUEST III BACCI/QUEST IV
Mar 18–Apr 9, 2003 Feb 28–Apr 4, 2004 Apr 5–May 16, 2005
Hyytiälä Heidelberg Hyytiälä
n≈1 6 (38%) 6 (60%) 9 (45%)
n≈1.5 4 (25%) 3 (30%) 2 (10%)
n≈2 5 (31%) 1 (10%) 6 (30%)
n≈2.5–3 1 (6%) – 3 (15%)
mean R 0.85 0.75 0.82
median A (1/s) 1.0e-06 1.1e-05 2.4e-07
median K (cm 3 /s) 4.5e-13 3.9e-12 3.2e-14
Of these, the possibility (iii) is the most probable one. Option (i) can be ruled out,
because due to its small saturation vapour pressure, sulphuric acid always condenses
on particles. Therefore, if sulphuric acid participates in nucleation, it will also participate
in the growth of freshly nucleated particles. Overall, the participation of organic
compounds in nucleation or early growth is probable, e.g. the presence of organic acids
has been observed to enhance nucleation in laboratory (Zhang et al., 2004).
4.2 Activation and kinetic nucleation mechanisms
None of the previously presented nucleation theories — classical binary H 2 SO 4 -H 2 O or
ternary H 2 SO 4 -NH 3 -H 2 O nucleation — is able to explain the small correlation exponents
between new particle formation rate and [H 2 SO 4 ]. Classical binary and ternary
nucleation theories would predict correlation exponents of ∼4–10, and based on the
nucleation theorem (Eq. 14) this would mean that there are 4–10 H 2 SO 4 molecules in
the critical cluster. The correlation exponents 1–2 observed in the field measurement
data (papers I and II) are far below this.
To explain the observed linear relationship between new particle formation and sulphuric
acid concentration, Kulmala et al. (2006) proposed a new nucleation mechanism,
”activation nucleation”, in which the nucleation rate is directly proportional to
the sulphuric acid concentration:
J act = A [H 2 SO 4 ]. (46)
Here A is an empirical activation coefficient (units 1/s), which will be determined
according to measurement data.
In activation nucleation, nucleation is thought to happen via activation of small (∼1
nm) clusters, which after activation reach the critical radius and start to grow larger by
condensation of sulphuric acid and other vapours available. Two possibilities for this
activation process have been suggested: (i) small clusters which contain one sulphuric
acid molecule are activated via heterogenous nucleation of some other substance or by
surfacechemical reactions; or(ii)smallclustersofunspecifiedcomposition(e.g. organic
clusters) are activated when a sulphuric acid molecule hits them. These both processes
would generate a linear relationship between the nucleation rate and the sulphuric acid
concentration. Even though at present the theory of activation nucleation is somewhat
ambiguous, it provides a simple parameterisation that can be tested and utilized in
modelling nucleation. The physical and chemical details of the nucleation process
are lumped together in the activation coefficient, which so far is merely an empirical
To explain the squared relationship between new particle formation and sulphuric acid,
the ”kinetic nucleation” scheme was proposed (paper I), in which the nucleation rate
is proportional to the square of H 2 SO 4 concentration:
J kin = K [H 2 SO 4 ] 2 , (47)
where K is an empirical kinetic coefficient (units cm 3 /s). This nucleation mechanism
has the functional form of collision-limited kinetic nucleation of sulphuric acid, where
stable clusters are formed by collision of two H 2 SO 4 molecules (McMurry and Friedlander,
1979). However, here the prefactor K is kept as a free empirical parameter, which
will be determined based on measurement data. Similarly as in activation nucleation,
the kinetic coefficient K contains the details of the nucleation process: specifically the
probability that a collision of two sulphuric acid containing molecules/clusters results
in the formation of a stable cluster. The upper limit for K is set by the collision frequency,
which is obtained from the kinetic gas theory (Eq. 15). For H 2 SO 4 molecules
at T = 293K, the kinetic collision frequency is about 3·10 −10 cm 3 s −1 .
In papers I and II these nucleation mechanisms were examined and the values of
the nucleation coefficients A and K were determined for the first time. We fitted J 3
and J 1 with the sulphuric acid concentration and determined values for the nucleation
coefficients which produced the best fit (see Figs. 5 and 6 in paper I). The fitting
was performed separately for each day, thus obtaining a distribution of daily A and
K coefficients. Due to scatter in the data, on many days it was hard to decide which
nucleation mechanism (activation or kinetic) fitted better. Therefore, for every day the
values of both coefficients were determined.
Themedian values oftheactivationandkinetic coefficients foreach campaignarelisted
in Table 1. The values of the activation and kinetic coefficients showed large variation
from day to day: inside one data set (each the length of a couple of months) the
nucleationcoefficients variedover 1–2ordersofmagnitude. ThevaluesofAandK were
about an order of magnitude higher in Heidelberg as compared to Hyytiälä, probably
related to Heidelberg being more affected by anthropogenic pollution such as ammonia
whichcouldenhancenucleation. Thesulphuric acidconcentrationsweremeasured with
the same method (CIMS, see Sect. 3.1) during all the campaigns, but the individual
instruments were different. This causes some uncertainty to the comparison of the data
sets, as there may be some offset between the different instruments.
The variations of the A and K coefficients during different measurement campaigns
are compared in Figure 14, with also the values reported by Nieminen et al. (2009)
for EUCAARI 2007 campaign in Hyytiälä and by Paasonen et al. (2009) for Hohenpeissenberg
station in Germany included. The nucleation coefficients are similar in
magnitude for Hyytiälä and Hohenpeissenberg, although some variations between the
three Hyytiälä data sets is observed. The values of A and K are about an order of
magnitude higher in Heidelberg as compared to Hyytiälä. In Hohenpeissenberg data
set the variation of the coefficients is much larger than in Hyytiälä and Heidelberg:
over 3 orders of magnitude for A and up to 5 orders of magnitude for K. This is probably
related to the Hohenpeissenberg data set being 1.5 years long, thus covering all
seasons, while measurements in Hyytiälä and Heidelberg were from spring-summertime
In comparison with the earlier results by Weber et al. (1995, 1996, 1997), our study
shows strikingly similar results. Weber et al. (1996) reported a prefactor φ to the
kinetic collision frequency of sulphuric acid-water clusters of φ = 0.001 for Mauna
Loa and φ = 0.003 for Idaho Hill, with which the nucleation rate would be: J nuc =
φK kin [H 2 SO 4 ] 2 . With K kin = 3 · 10 −10 cm 3 s −1 , Weber’s prefactor (corresponding to
our nucleation coefficent K) would be 3–9 ·10 −13 cm 3 s −1 , which is in the same range
with our values for the kinetic coefficient in Hyytiälä.
The physical and chemical details of the nucleation prosess are hidden behind the empirical
activation and kinetic coefficients. The large variation in A and K implies that,
besides sulphuric acid, there are other factors that affect the atmospheric nucleation
The existence of pure ”activation days” with linear correlation (e.g. the day in Fig.
12) and pure ”kinetic days” with squared correlation with [H 2 SO 4 ] (e.g. the day in
Fig. 3b of paper II), implies that there are different (at least two) nucleation/initial
growth mechanisms working on different days with varying ambient conditions. The
conditions affecting the nucleation mechanism can be the level of [H 2 SO 4 ], presence of
organic compounds (oxidation products of VOCs), ammonia or amine concentrations,
temperature, relative humidity etc.
After papers I and II, a few studies on the connection of NPF with sulphuric acid
have been published. Kuang et al. (2008) investigated the sulphuric acid correlations
at several locations by applying somewhat different methods for J 3 calculation (Eq.
31) and correlation analysis than in this thesis. They found that kinetic nucleation
(with exponent very close to 2) was explaining nucleation in all studied places. In their
analysis, Kuang et al. combined the data points from different days into one data set,
A (s −1 )
25 % − 75 %
Min − Max
K (cm 3 s −1 )
25 % − 75 %
Min − Max
Hyy Q2 Hyy Q4 Hyy 2007 Hei Q3 Hohenp
Hyy Q2 Hyy Q4 Hyy 2007 Hei Q3 Hohenp
Figure 14: The values of activation (A, left) and kinetic (K, right) coefficients during
five measurement campaigns: QUEST II, QUEST IV and EUCAARI 2007 (Nieminen
et al., 2009) at the Hyytiälä SMEAR II station; QUEST III in Heidelberg, Germany;
and HAFEX at the Hohenpeissenberg station, Germany (Paasonen et al., 2009).
for which the correlations were determined, whereas in the studies of this thesis the
correlations were investigated separately for each day.
Paasonen et al. (2009, 2010) examined the effect of organic vapours in activation and
kinetic nucleation mechanisms. The nucleation coefficients A and K were observed
to correlate positively with monoterpene oxidation products, but no such correlation
existed for the nucleation rate (J 1.5 ) (Paasonen et al., 2009). A comprehesive study of
data from Hyytiälä, Hohenpeissenberg (Germany), Melpitz (Germany) and San Pietro
Capofiume (SPC, Italy) showed that overall, kinetic sulphuric acid nucleation explains
nucleation well in all other places than Hohenpeissenberg, where the effect of organics
is dominant. However, even at the sulphuric acid-dominated sites (Hyytiälä, Melpitz,
kinetic nucleation of H 2 SO 4 ) improved the nucleation rate prediction (Paasonen et al.,
2010). The importance of organic vapours very probably explains the high variation
for A and K in Hohenpeissenberg shown in Fig. 14.
There are indications that ammonia or amines (Petäjä et al., 2011; Zhao et al., 2011;
for atmospheric nucleation. Brus et al. (2011) have reported laboratory measurements
of H 2 SO 4 -H 2 O nucleation, in which the correlation exponent was observed to decrease
with increasing temperature (from n = 2.2 at 5 ◦ C to n = 1.2 at 25 ◦ C).
In papers I–II the exponent of the correlation J 1 ∼ [H 2 SO 4 ] n (the slope of the log(J 1 )
vs log([H 2 SO 4 ]) plot) was interpreted as the number of H 2 SO 4 molecules in the critical
cluster, based on the approximate version of the nucleation theorem (Eq. 14). According
to current knowledge, this conclusion does not hold: if the Gibbs free energy curve
haslocal minima, thebasic nucleation theorem isnot valid, andat least theapproximation
n ∗ +1 ≈ n ∗ can not be done, when n ∗ is small. However, the correlation exponent
can be interpreted as giving information on the rate limiting step in atmospheric NPF
(cluster formation or their growth): this step seems to be proportional to the H 2 SO 4
concentration to the power between 1 and 2.
When papers I and II were published, there existed a remarkable gap between atmospheric
and laboratory measurements of nucleation (see Sect. 2.2.3): the slope of
log(J nuc vs log([H 2 SO 4 ]) curves were significantly higher in the laboratory (order of
4–10) than in the atmosphere. This discrepancy has been overcome by recent advances
in measurement technologies of 1–3 nm particles, and the slopes of 1–2, as
observed in atmospheric measurements, have been reproduced also in laboratory conditions
(Sipilä et al., 2010).
Korhonen et al. (2010) made a computational study on the sulphuric acid correlations,
investigating the accuracy of the analysis methods to determine the exponent of nucleation
andthe values of the nucleation coefficients (A and K). The result was that there
are several uncertainties in the analysis procedure, especially in the determination of
nucleation rates from the particle formation rates at 3 nm. Therefore, the correlation
exponents and values of the nucleation coefficients determined with several different
steps in the data analysis procedure should be interpreted with caution: at least noting
that they contain significant error bars.
Despite their deficiencies (the large variation of A and K even within the same data
set), thedeveloped parameterisations foractivationandkinetic nucleation have already
been used quite widely in globalaerosol andclimate models (e.g. Spracklen et al., 2006,
2008; Makkonen et al., 2009). The parameterisations capture quite well nucleation
happening in the atmospheric boundary layer.
Summarizing, the atmospheric particle formation rate is observed to depend on the
sulphuric acid concentration to the power 1–2 (papers I and II). According to current
knowledge, the kinetic nucleation (with exponent 2) seems to be most widely valid,
together with co-nucleation of sulphuric acid and organics. In some places, nucleation
may be dominated by organic compounds (Paasonen et al., 2010). Pure activation
nucleation (with linear correlation with H 2 SO 4 ) seems to be a special case, which
certainly acts in some conditions, but overall it happens rather rarely. In the future,
aerosol mass spectrometric measurements will probably reveal the constituents of the
nucleated clusters. The final goal is to develop a parameterisation and a theoretically
consistent framework that captures all important factors affecting the atmospheric
4.3 The effect of relative humidity on the nucleation rate
with low relative humidity (RH) (e.g. Birmili et al., 2000; Boy and Kulmala, 2002;
Hyvönen et al., 2005). This has been observed consistently in several locations, but
no solid explanation for the observation has been given so far. It has been speculated,
that the main reason would be the increased coagulation and condensation sink, due
to background particles’ diameter increase when they take up water from humid air.
This leads, on one hand, to increasing coagulational scavenging of small, nucleated
particles; on the other hand, increased condensation sink decreases the concentrations
of condensable vapours, thereby hindering nucleation and initial particle growth. Both
these effects act in the same direction, and prevent particle formation.
In contrast to atmospheric observations, in laboratory measurements of nucleation in
H 2 SO 4 -H 2 O or H 2 SO 4 -NH 3 -H 2 O-system, the nucleation rates are consistently observed
to increase with relative humidity (Berndt et al., 2005; Brus et al., 2011; Benson et
al., 2008, 2009). Also from a theoretical point of view this would be expected. As
atmospheric particle formation is thought to happen via co-nucleation of sulphuric
acid and water or via a ternary mechanism involving also ammonia, increasing water
vapour concentration should enhance nucleation as the formation energy of a critical
cluster islowered whentheconcentration(orsaturationratio)ofanucleating substance
increases (Vehkamäki et al., 2002, Merikanto et al., 2007).
In paper III, the reasons behind the RH-inhibition of new particle formation were
examined in detail with the aid of field measurement data, theoretical calculations
and aerosol dynamical simulations. A new hypothesis for RH-inhibiting effect was
presented: decreased solar radiation in humid conditions might limit sulphuric acid
production and thereby lead to smaller nucleation rates. The purpose was to find out,
which of the following effects is the dominating one in preventing NPF at high RH:
i) effect of RH on H 2 SO 4 concentration via reduced OH concentration (reduced
solar radiation) at high RH;
ii) effect of RH on H 2 SO 4 concentration via increased condensation sink at high RH;
iii) effect of RH to J 3 through increased coagulation sink at high RH.
New hypothesis for the RH-inhibiting effect on NPF
(J 1.5 ) and sulphuric acid concentrations presented in Fig. 15. When the points in J 1.5
vs [H 2 SO 4 ] plot were colour scaled according to relative humidity, a clear dependence
on RH emerged: nucleation rates were highest when RH was lowest and vice versa.
Whenplottedwithabsolutehumidity (water vapourconcentration), nosuch separation
of points happened as with RH.
O (%o) as colour code (QUEST II)
(cm −3 s −1 )
(cm −3 s −1 )
6 a.m. − 6 p.m.
10 4 10 6
] (cm −3 )
RH (%) as colour code (QUEST II)
6 a.m. − 6 p.m.
10 4 10 6
] (cm −3 )
Figure 15: Nucleation rate versus sulphuric acid (in log axes), colour scaled according
toabsolutehumidity(H 2 Oconcentration, left)andrelativehumidity(RH,right)during
QUEST II campaign at the Hyytiälä SMEAR II station. The lines correspond to the
linear and squared correlation between J 1.5 and [H 2 SO 4 ].
The observation shown in Fig. 15 led us to present a hypothesis that the RH-effect
on the nucleation rate is mediated through sulphuric acid concentration: high RH
may prevent H 2 SO 4 formation via decreased photochemistry due to decreased sunlight
reaching the ground on hazy or partially cloudy days with high RH. Decreased solar
radiation leads to decreased formation of OH radicals, which further affects the formation
of H 2 SO 4 through reaction of SO 2 and OH (see Sect. 2.3). As the nucleation rate
is controlled by sulphuric acid (as reported in papers I and II), smaller sulphuric acid
concentrations are directly transferred to smaller nucleation rates.
Data analysis revealed that at RH > 60 % the sulphuric acid concentrations decreased
with increasing RH. Especially the highest H 2 SO 4 concentrations were totally missing
at RH > 60 % (see Fig. 1 in paper III). The SO 2 concentration was observed to
be rather independent of RH. Instead, OH and UV showed very similar correlation
with RH as H 2 SO 4 : both the OH concentration and UV radiation intensity started
to decrease above a RH of 60 %. Taken together, this data suggests that RH limits
nucleation through limiting UV-B and OH, and thereby sulphuric acid production.
The decreasing effect of RH on UV radiation can be explained as follows. At humid
conditions, the probability of cloud and fog formation increases, and in the presence
of clouds the UV radiation reaching the lower atmosphere (boundary layer) decreases.
The relationship between cloudiness and RHwas investigated using a 30-year long data
set oflow level clouds collected by theFinnish Meteorological Institute at theJokioinen
weather station. As expected, the amount of low level clouds was negatively correlated
with RH. Interestingly, there seemed to be a threshold value of RH (about 40–60 %)
above which cloudiness started to increase steeply with RH, especially around midday
hours (see Fig. 5 in paper III). A plot of global radiation versus RH in the Jokioinen
data set showed a similar decreasing trend with RH as in the Hyytiälä QUEST II data
set, and a mirror-like behaviour as compared to cloudiness. It is worth noting, that a
O (%o) as colour code (EUCAARI 2007)
6 a.m. − 6 p.m.
RH (%) as colour code (EUCAARI 2007)
6 a.m. − 6 p.m.
(cm −3 s −1 )
10 4 [H 2
] (cm −3 )
(cm −3 s −1 )
10 4 10 6 10 8
10 4 10 6 10 8
] (cm −3 )
Figure 16: Nucleation rate versus sulphuric acid, colour scaled according to absolute
humidity(H 2 Oconcentration, left)andrelativehumidity(RH,right)duringEUCAARI
2007 campaign at the Hyytiälä SMEAR II station. The lines correspond to the linear
and squared correlation between J 1.5 and [H 2 SO 4 ].
similar threshold at RH = 40–60 % was observed for all variables: H 2 SO 4 , OH, UV,
global radiation and cloudinesss. The cloudiness data supports the hypothesis that the
RH limits the H 2 SO 4 concentration through limiting OH production, and this effect
is because of decreased UV radiation reaching the ground due to cloudiness in humid
The study presented in paper III was based on data from the QUEST II campaign
from Hyytiälä. The similar correlation of J 1.5 and H 2 SO 4 with RH (but not with H 2 O
concentration) is seen also for QUEST IV and EUCAARI 2007 data sets (see Fig.
16) from Hyytiälä in spring 2005 and 2007, respectively. This gives confidence that
the results are more generally valid, at least in conditions at the Hyytiälä SMEAR II
Another reason for the observed anti-correlation of OH and UV with RH could be,
that these variables have opposite diurnal profiles: UV radiation (and thus OH) peaks
at noon, whereas RH has minimum at noon/afternoon, when temperature and water
saturation concentration are the highest. This results in an apparent anticorrelation
between UV (and OH) with RH, without a necessary causal correlation between these
variables. The effect of opposite diurnal variations makes it difficult to distinguish how
much of the observed correlation is explained by cloudiness and how much is only due
to diurnal variations. In paper III it is suggested that opposite diurnal cycles would
be the main reason for the anticorrelation of OH and UV (and H 2 SO 4 ) with RH, and
the effect of cloudiness would be a minor effect.
Effect of increased condensation and coagulation sink
At humid conditions aerosols experience hygroscopic growth: they take up water,
thereby increasing their diameter and surface area. The DMPS measures the particle
size distribution as a dry distribution at about RH = 30 % prevailing inside the
instrument. The hygroscopicity of particles then has to be taken into account using
a parameterisation for particle wet diameter, in this case with a parameterisation by
Laakso et al. (2004) for Hyytiälä conditions. As an example, from RH of 30 % to 90 %
hygroscopic growth increases the condensation and coagulation sinks by about a factor
of 3 (paper III).
The increased condensation sink (CS) increases the loss rate of sulphuric acid, leading
to smaller H 2 SO 4 concentrations. This is further transferred to a smaller nucleation
rate and particle formation rate at 3 nm, J 3 . The increase in coagulation sink (CoagS),
in turn, increases the coagulational scavenging of small clusters. The probability of a
cluster surviving from the nucleation size (1–1.5 nm) to 3 nm size becomes smaller,
leading to a smaller particle formation rate at 3 nm (J 3 , as described by Eq. 37 or 43).
The effect of increased coagulation sink was examined by theoretical calculations performed
using the new form of the Kerminen-Kulmala equation, Eq. 43 (Lehtinen et
al., 2007). We calculated how much J 3 decreases from the nucleation rate J 1.5 at different
relative humidities, when wet-CoagS is calculated with the parameterisation by
Laakso et al. (2004). The result was that increased CoagS could suppress new particle
formation, provided that the particle growth rate is low and the coagulation sink
(background aerosol concentration) is high (”extreme case” in paper III). In such
conditions, J 3 decreased by 1–3 orders of magnitude from J 1.5 when RH increased from
10 to 90 %, indicating that at high RH CoagS could mask the new particle formation
event from observation at 3 nm. However, at average conditions of typical growth rate
and CoagS, the decrease from J 1.5 to J 3 was smaller, and not enough to suppress the
increased CS were further investigated by performing aerosol dynamical simulations.
%, based on the observed correlation of OH with RH (Fig. 4 in paper III) and
analysis from a chemical model (Boy et al., 2005). The modelling results showed that,
of these variables, the particle formation rate J 3 was most sensitive to the reduced
OH levels, as decreased OH directly leads to smaller sulphuric acid concentrations and
nucleation rates. The effects of increased CS (through decreased H 2 SO 4 concentration)
and increased CoagS (through the coagulational scavenging of small clusters) on J 3
were similar in magnitude, but these effects were significantly smaller than that of
reduced OH concentration.
In conclusion, paper III reports the finding that RH seems to limit the nucleation rate
by limiting OH and H 2 SO 4 production at high relative humidities. In comparison to
OH-effect, the earlier proposed mechanisms for the RH-inhibiting effect, increased condensation
and coagulation sinks, are shown to have smaller contribution in suppressing
new particle formation. The effect of RH on OH could be related to cloudiness at
high RH: cloud and haze droplets increase the scattering of sunlight, leading to less
radiation reaching the ground and smaller OH production rates. However, it is possible
that the observed anticorrelation of H 2 SO 4 and RH is mainly due to opposite
diurnal profiles of UV radiation and RH. Paper III concludes that ”even though at
first glance RH appears to limit NPF, this appearance is due to its anticorrelation with
The study of paper III demonstrates how difficult it is to distinguish real reasons and
causal relationships behind an observed correlation in atmospheric data, when almost
all variables have a diurnal variation related to sunlight. Actually, paper III provokes
even more questions than it answers. A continuing study would be needed, with more
sophisticated data analysis methods to separate the diurnal variation from the other
variations in the data. Also, it would be interesting to repeat the investigation at other
sites, to find out how generally the proposed mechanism of supression of new particle
formation by reduced OH production at high RH is valid.
4.4 Modelling the connection between sulphuric acid and particle
In papers I and II the strong correlation between new particle formation and gasphasesulphuric
acidconcentration wasstudiedbasedondatameasured atfieldstations
in Hyytiälä and Heidelberg. The activation and kinetic nucleation mechanisms were
proposed as explanations for the linear or squared relationship between particle formation
at 3 nm and sulphuric acid concentration. In order to study in more detail this
correlation, aerosol dynamical simulations were performed (paper IV). The purposes
of the simulations were:
(i) to find out whether other factors than the nucleation mechanism, such as condensation
and coagulation, affect the correlations of J 3 and N 3−6 with [H 2 SO 4 ];
(ii) to examine how the correlation with [H 2 SO 4 ] changes as particles grow from
nucleated size (1–2 nm) to 3 nm;
(iii) to find the conditions which would yield the observed linear correlation (on some
days) between particle number concentration N 3−6 and sulphuric acid.
Thesimulations were performedwiththeUHMAmodel using threedifferent nucleation
mechanisms: activation, kinetic and ternary nucleation. The condensing vapours were
sulphuric acid and an organic vapour with nano-Köhler mechanism for condensation.
Sulphuric acid had a sinusoidal profile with maximum of 5–7 ·10 6 cm −3 at noon, corresponding
to typical sulphuric acid concentrations in Hyytiälä, whereas the organic
vapour had a constant concentration of 10 7 cm −3 . The relative humidity was 50 % and
ammonia (NH 3 ) concentration 5 ppt. To investigate how the correlation of J 3 andN 3−6
with [H 2 SO 4 ] depends on the particle condensational growth rate and the size at which
nucleation is happening (objective ii), we varied the saturation vapour concentration of
the organic vapour (c sat,org , which affects the profile of the growth rate as a function of
particle diameter), and the size of the nucleated cluster (d nuc ), respectively. In total, a
high number of sensitivity runs were performed; paper IV reports in more detail the
results of six case studies representing the main features of the simulations (Fig. 17).
The correlations with sulphuric acid concentrations were studied separately for the
nucleation rate, the particle formation rate at 3 nm and the number concentration of
3–6 nm particles. The correlation exponents were determined for J nuc ∼ [H 2 SO 4 ] nnuc ,
J 3 ∼ [H 2 SO 4 ] n J 3 and N 3−6 ∼ [H 2 SO 4 ] n N 3−6 by finding the slope of the log-log curve.
Figure17: Simulated new particleformationevents applying different nucleation mechanisms:
activation (top), kinetic (middle) and ternary nucleation (bottom). The left
column (a, c, e): c sat,org = 10 6 cm −3 and nano-Köhler mechanism for the condensable
organic vapour; the right column (b, d, f): c sat,org = 0 cm −3 . The white horizontal line
shows the 3 nm border.
Table 2: The correlation exponents n J3 and n N3−6 for J 3 ∼ [H 2 SO 4 ] n J 3 and N 3−6 ∼
[H 2 SO 4 ] n N 3−6, for events simulated by the UHMA model (Fig. 17), using different nucleation
mechanisms and condensing organic vapour properties. The nucleated cluster
size was in all cases d nuc = 1 nm.
Activation nucleation Kinetic nucleation Ternary nucleation
n nuc = 1 n nuc = 2 n nuc ≈ 5.6
c sat,org = 10 6 cm −3 n J3 = 3.2 n J3 = 3.4 n J3 = 5.6
n N3−6 = 2.3 n N3−6 = 2.3 n N3−6 = 4.1
c sat,org = 0 cm −3 n J3 = 1.3 n J3 = 2.1 n J3 = 5.0
n N3−6 = 1.2 n N3−6 = 1.7 n N3−6 = 4.0
for these three quantites (Table 2). Especially with activation nucleation, which has
nucleation exponent n nuc = 1, the correlation exponent could increase by 1–2 units for
J 3 and N 3−6 . Generally, the exponent for N 3−6 correlation was smaller than for J 3 .
In case of ternary nucleation, the correlation exponent for N 3−6 was even smaller than
the nucleation exponent.
These changes in sulphuric acid correlation exponents may seem peculiar. However,
they are explained by aerosol dynamical processes happening during the growth from
nucleation size at 1–2 nm to 3–6 nm. The simulations revealed that most important
for the change of the correlation exponent is the particle growth rate between 1–3
nm, which is both size and time dependent. The size dependence of the growth rate
with different values of organic vapour saturation concentration (c sat,org ) is presented
in Fig. 18. At high saturation concentration (c sat,org = 10 5 –10 6 cm −3 ), the growth of
the smallest particles (1–1.5 nm) is solely due to sulphuric acid, and the organic vapour
starts to condense gradually between 1.5–4 nm, following the nano-Köhler mechanism
(see Fig. 5 in paper IV). When the organic saturation concentration decreases, the
growth rateof small particles increases, as organicvapour starts to condense onsmaller
and smaller particles. At c sat,org = 0, the organic vapour condenses with the maximum
flux (not limited by the Kelvin effect).
With activation nucleation, preserving the exponent of nucleation for J 3 and N 3−6
required either i) fast growth of the nucleated particles, or ii) nucleation happening at
2 nm size. For the first requirement, the nano-Köhler mechanism (with non-negligible
saturation concentration) for organic vapour condensation was not alone sufficient to
increase the growth rate of the smallest particles, but a negligible saturation (c sat,org ≤
10 2 cm −3 ) concentration was required to get high enough growth rate (see Fig. 18). In
both these cases, particles grow fast from nucleation size to 3–6 nm, so that also the
sulphuric acid correlation ”has no time to change much”.
In addition to condensational growth, the coagulation loss of freshly nucleated particles
affects the correlation of J 3 and N 3−6 with sulphuric acid. This question was not
addressed in the study of paper IV. As coagulation becomes important at high nucle-
ation rates, it was speculated that the different behaviour of the correlation exponents
in case of ternary nucleation (exponent decreases from J nuc to J 3 and N 3−6 ) could
be caused by the effect of coagulation (the ternary mechanism causes more intense
nucleation, as seen in Fig. 17).
Growth rate (nm/h)
GR−total at t = 12 h
= 10 6 cm −3 (Case 1)
c = 10 5 cm −3
c = 10 4 cm −3
= 10 3 cm −3
c = 10 2 cm −3
c = 0 cm −3 (Case 2)
1 2 3 4 5 6 7 8
Particle diameter (nm)
Figure 18: The particle growth rate due to condensation of sulphuric acid and organic
vapour as a function of particle size in the simulations made with the UHMA
model. The different curves are for the different values of the organic vapour saturationconcentration(c
sat,org ). Theorganicvapourcondensationfollowedthenano-Köhler
Asaconclusion, thecorrelationwithsulphuric acidcanchangesignificantly during particle
growth from the nucleation size 1–1.5 nm to 3–6 nm, and therefore the correlation
exponents observed for J 3 or N 3−6 should not be interpreted directly as the exponent of
nucleation. However, modelling results showed that the correlation exponent can not
change very much, only by 1–2 units, and therefore ternary nucleation, having a correlation
exponent 4–6, can be most probably ruled out, at least for nucleation happening
in the boundary layer in boreal forest conditions. According to the results presented
in this thesis, one can safely say that the nucleation mechanism seems to involve sulphuric
acid and has a dependence on the sulphuric acid concentration to the power of
1–3. This result is supported also by laboratory studies with novel instrumentation
(Sipilä et al., 2010; Brus et al., 2011).
5 CCN activity of boreal forest aerosols
Aerosols are needed in cloud formation as seeds for water condensation, i.e. to act
as cloud condensation nuclei (CCN). An aerosol particle can act as a CCN, if its size
is bigger than the critical (threshold) diameter for irreversible water condensation to
happen. In the fast condensation of water, called activation, the CCN are converted to
cloud droplets. The critical size depends on the physical size of the particle (diameter)
and its chemical composition (solubility to water). Typically aerosol particles bigger
than 50–100 nm are potential CCN. It is probable, that a considerable fraction of
particles acting as CCN are produced by atmospheric nucleation events (Merikanto
et al., 2009; Kerminen et al., 2012).
Aerosol climate effects through acting as CCN are called the aerosol indirect effects
(Penner et al., 2004). In cloud formation, increasing CCN concentrations inside a cloud
cause a larger number of cloud droplets but smaller in size to be formed, assuming that
the same water amount is condensing on a bigger number of CCN. This has twofold
effects on cloud characteristics: i) smaller cloud droplets scatter solar radiation more
efficiently, resulting in a higher cloud albedo i.e. whiter clouds (first indirect effect)
and ii) smaller cloud droplets do not precipitate as easily, making the cloud lifetime
longer (second indirect effect). Thus, increasing aerosol concentrations imply whiter
and longer-lasting clouds, exerting a cooling effect on the climate (see Fig. 1). In
addition to these cooling effects, clouds scatter back infrared radiation coming from
the Earth’s surface. Also, black carbon and dust aerosols can form so called ”brown
clouds”, which are actually thick aerosol layers and not clouds. These brown clouds,
which are encountered in heavily polluted areas in Asia (India and China), absorb
solar radiation and via complex effects on atmospheric temperature, may have both
warming and cooling effects on the climate (semi-direct effects) (Ramanathan et al.,
2007; Koch and Del Genio, 2010).
Aerosol-cloud effects are one of the poorest understood parts of the climate system.
According to current knowledge, aerosols have during the past 50–100 years caused
a significant net cooling effect on the climate, thus masking part of the warming by
greenhouse gases (Andreae et al., 2005; Makkonen et al., 2012).
The possibility to cool the climate artificially, e.g. by inserting sulphate aerosols in
to the stratosphere (where they directly scatter sunlight) or sea-salt aerosols to the
marine troposphere (where they affect the formation of stratocumulus clouds), has
been suggested as a possible way to counteract climate warming. This is called geoengineering,
and despite the big risks associated with it, it has become a serious path
in climate research (e.g. Partanen et al. (2012)). Also for this reason, understanding
the aerosol-cloud interactions is crucial.
It has been proposed that Nature itself could also have a feedback mechanism through
aerosols which would decrease the climate warming (Kulmala et al., 2004c; Tunved
et al., 2008; Paasonen et al., 2013). Natural aerosols are to a big extent formed on
continental areas with forests and other vegetation. Formation of secondary organic
aerosols could increase in the warming climate, as most of the organic vapour emissions
increase with temperature. This would increase direct scattering of solar radiation and
affect cloud formation, thus having a cooling feedback effect on climate.
Boreal forest areas, covering 8 % of the Earth’s surface, are even a globally important
source of secondary organic aerosol (SOA) particles (Tunved et al., 2006a), which
have climatic effects at least on a regional scale (Lihavainen et al., 2009). In paper
VI the ability of boreal forest aerosols to act as cloud condensation nuclei was
investigated based on 1 year of continuous CCN concentration measurements at the
HyytiäläSMEARIIstation. Inaddition, concurrent hygroscopicitymeasurements were
analysed, to get more information on the CCN activity of aerosols in Hyytiälä.
5.1 Seasonal variation of CCN properties at the Hyytiälä
SMEAR II station
The measured CCN concentration at a certain supersaturation is determined by the
aerosol number concentration, the aerosol size distribution (whether there are more
large, CCN active particles or more small, non-CCN-active particles), and the chemical
composition(thehygroscopicity) oftheparticles. Thechemical compositiondetermines
the critical diameter for cloud droplet activation.
Measured CCN concentrations were observed to have a clear seasonal variation, with
highest concentrations inthesummertime (Fig. 2inpaper VI).InJune-JulytheCCN
concentration was at least double the concentration in December-January. Also the
activated fraction (calculated in this study as the total fraction of particles activated to
cloud droplets, F act = N CCN /N CN , where N CN is the total particle number concentration)
had a maximum in summertime. The seasonal variation of the critical diameter
was a bit different, but it also had the smallest values during the growing season in
spring-summer. These findings indicate that, on average, the aerosol particles in the
summertime boreal forest are more hygroscopic and more CCN-active than aerosols in
wintertime. In summertime, aerosols are expected to contain a larger fraction of oxidation
products of organic substances emitted from the forest; the high CCN activity
of the summertime aerosol particles in Hyytiälä suggests that these organics are highly
The critical diameter (d crit ) for cloud droplet activation was determined in this study
by two different methods. First, d crit was determined from CCN concentrations and
particle size distribution (DMPS) data by simply integrating the size distribution from
the largest particle size towards smaller sizes, until the concentration matches the
measured CCN concentration:
d i =d crit
N i = N CCN , (48)
where the lower size limit corresponds the critical diameter. In this method it is
assumed that particles are internally mixed (i.e. particles of certain size have the same
Figure 19: Average critical diameters as a function of water supersaturation for
Hyytiälä aerosol, estimated from CCNC and HTDMA data (error bars indicate the
standard deviations in the one year data set). Laboratory measurements for secondary
organic aerosol (α-pinene and trimethylbenzene, TMB) are shown for comparison (Duplissy
et al., 2008). Lines show the theoretical values from the kappa-Köhler equation
for pure ammonium sulphate particles and for a range of SOA kappa values.
chemical composition), all particles larger than d crit are activated (i.e. differences in
chemical composition are neglected) and the activation probability behaves as a step
function at d crit .
Second, the critical diameter was estimated from the hygroscopicity measurements
(HTDMA) using kappa-Köhler theory (see Sect. 2.4). The value of the hygroscopicity
parameter κ (kappa) was determined from HTDMA-data (for conditions S < 1), and
after that the value of the critical (dry) diameter was calculated from Eq. 29 for the
supersaturations corresponding to CCN measurements (SS = 0.1–1.0 %).
The critical diameters determined by these two methods corresponded well to each
other, the mean values being ∼50 nm, ∼80 nm and 150–200 nm at SS of 1.0 %, 0.4
% and 0.1 %, respectively. While there were differences between daily and monthly
values, on average both methods produced very similar behaviour of d crit as a function
of supersaturation (see Fig. 19 and Table 1 in paper VI). The points fall nicely
on the theoretical slope of −2/3 on the log-log plot (d crit ∼ SS −2/3 ). The determined
critical diameters arenotfar fromthelaboratoryresults forα-pinenesecondary organic
aerosol. In Hyytiälä, α-pinene is one of the main monoterpenes emitted by the forest.
The presence of sulphate in Hyytiälä aerosols makes the critical diameters somewhat
lower than for pure organic aerosol.
The mean kappa parameter, as determined from HTDMA measurements, was 0.18.
This corresponds to estimated fractions of 84 % organics (κ = 0.1) and 16 % sulphate
(κ = 0.6). These fractions are in line with other estimates of the organic fraction
of Hyytiälä aerosols (Boy et al., 2005; Jimenez et al., 2009). Of course, this division
to only two consituents (organics and sulphate) is very rough. There are certainly
also less-hygroscopic organics (with κ < 0.1) or purely non-hygroscopic aerosols such
as black carbon present in Hyytiälä aerosol. The value of 0.18 is an average over all
supersaturations (0.1–1.0 %), and there are most probably differences in the κ values
between different particle sizes. This is reflected also in Fig. 19: at high supersaturations
the points start to deviate from the same straight line with slope −2/3.
The value determined for the κ-parameter (κ = 0.18) can be utilised in modelling the
concentrations of potential CCN in boreal forest. To capture the seasonal variation
of CCN concentrations, a seasonal profile for κ would be needed. This remains to be
determined in future studies.
The comparison of the two methods for determination of the critical diameter showed,
that even the simplified method of integrating the size distribution is capable of giving
at least a rough estimate of the treshold diameter for CCN activation. This is in line
with earlier results, which report that the particle size distribution dominates over
the chemical composition in determining the CCN concentrations (Dusek et al., 2006;
Quinn et al., 2008). In principle, the simplified integration method should give an
upper limit to d crit , because all particles larger than that size are assumed to activate,
regardless their chemical composition.
5.2 Effect of new particle formation on cloud condensation
Figure 20 shows an example of a period with several new particle formation (NPF)
events, together with the measured CCN concentrations, the activated fraction and
critical diameter (determined from the CCN-concentration and particle size distribution
data by Eq. 48). The CCN concentrations increase constantly during these NPF
days, even though the total number concentration (CN) is approximately constant.
This indicates that NPF events are producing significant numbers of particles to the
CCN-active size range. The increase in CCN concentration is more pronounced for the
three highest supersaturations (SS ≥ 0.4 %), which (due to smaller critical diameters)
are more affected by the growing nucleation mode.
The effect of new particle formation on CCN concentrations was further studied by
computing the average diurnal variation of the CCN concentration, activated fraction
and critical diameter separately on new particle formation event days and non-event
days (see Figs. 7–9 in paper VI). The diurnal variation was examined for a two-day
period, because the nucleation mode typically grows to CCN active sizes (to 50–100
nm) by the end of the NPF day. Nucleation events were observed to cause an increase
in CCN concentrations, which started in the evening of the NPF event day and lasted
untiltheendofnextday(Fig. 21). AmoderateincreaseinCCNnumberwasobservable
even at the smallest supersaturations, indicating that nucleation is really capable of
producing CCN-active particles.
20/04 21/04 22/04 23/04 24/04
) (cm −3 )
10 100 1000 10000 100000
CCN or CN [cm −3 ]
20/04 21/04 22/04 23/04 24/04
20/04 21/04 22/04 23/04 24/04
SS = 0.1 %
SS = 0.2 %
SS = 0.4 %
SS = 0.6 %
SS = 1.0 %
20/04 21/04 22/04 23/04 24/04
Figure 20: Comparison of the particle size distribution data and cloud condensation
nuclei (CCN) data for a period with four consecutive new particle formation days in
Hyytiälä (20.4.-23.4.2009). (a) The time evolution of particle size distributions, (b)
CCN and total particle (CN) concentrations, (c) the activated fraction (CCN/CN),
and (d) the critical diameter estimated from CCN and particle size distribution measurements.
Elevated CCN concentrations due to new particle formation events have been reported
also in other studies (Lihavainen et al., 2003; Kuwata et al., 2008; Wiedensohler et al.,
2009; Asmi et al., 2011).
The study of paper VI was based on analysing ground-based measurements. It must
be noted, that the link between organic aerosols formed in the atmospheric boundary
layer and clouds formed in the upper part of the troposphere is not straightforward.
To really influence cloud formation, aerosols should travel from the forest up to the
height of 1–2 km. Airborne measurements are needed to find out whether the CCN
inside tropospheric clouds originate from the boundary layer, or are formed by in-situ
nucleation in the upper troposphere.
CCN concentration (cm −3 )
SS = 0.4 %
00:00 12:00 00:00 12:00 00:00
Time (hour of day)
Figure 21: Mean diurnal variation of CCN concentrations on two consecutive days,
compared between new particle formation event and non-event days at supersaturation
SS = 0.4 % (data points are averages over 1 year data from the Hyytiälä SMEAR II
6 Review of papers and the author’s contribution
Paper I investigates the correlation of sulphuric acid and new particle formation by
analysing field data measured during the QUEST II campaign in Hyytiälä, at the
SMEAR II station. The paper reports day-specific values for empirical activation and
kinetic nucleation coefficients for the first time. I made all the data analysis and was
responsible for writing the main parts of the article.
Paper II continues to study the correlation between sulphuric acid and new particle
formation utilizing data sets from the QUEST III and IV campaigns from Heidelberg
(Germany) and Hyytiälä (Finland). The methods for correlation analysis were developed
further in this paper. The values for activation and kinetic coefficients in these
data sets were determined. I made half of the data analysis and participated in writing
Paper III studies the effect of relative humidity on atmospheric particle formation
by combining data analysis and aerosol dynamical modelling. Utilizing the QUEST
II data set, the paper presents an anticorrelation of sulphuric acid concentration and
particle formation rate with relative humidity. Aerosol dynamical modelling is used to
investigate thereasonsfortheobserved anticorrelation, concluding thatrelativehumidity
suppresses nucleation due to decreased production of sulphuric acid. I participated
in the data analysis and assisted in finalizing the manuscript.
Paper IV examines factors affecting the correlation of sulphuric acid and particle
formation rate with the aid of aerosol dynamical modelling. Especially, the effect of
the nucleation mechanism and condensational growth on the observed correlation at 3
nm are investigated. The paper demonstrates that the correlation with sulphuric acid
can change significantly during the particle growth from nucleation size to 3 nm. I
made most of the simulation runs and data processing, and was responsible for writing
Paper V investigates the methods used to calculate particle formation rates from the
time evolution of the particle size distribution. The study is based on the analysis of
a simulated particle formation event. The paper compares different particle formation
rate calculation methods and gives a recommendation of the most appropriate one. I
participated in planning the paper, gave ideas for the data analysis and assisted in
writing the manuscript.
Paper VI presents an analysis of one-year measurements of cloud condensation nuclei
kappa were derived from the data. The seasonal variation of CCN concentrations and
critical diameters were investigated, as well as the effect of new particle formation on
them. I made most of the analysis related to CCN concentration measurements and
was the main author of the paper. The hygroscopicity data was analysed by other
7 Summary and conclusions
Particle formation from gaseous precursors is a major source of new particles in the
atmosphere. Due to their ability to scatter solar radiation and influence cloud formation,
aerosol particles cause a net cooling effect on the Earth’s climate, thus partly
counteracting the climate warming caused by greenhouse gases. The understanding of
atmospheric aerosol formation, their growth to climatically relevant sizes and role in
cloud formation is crucial for reliable modelling of the climate system.
Atmospheric new particle formation or nucleation is a complex phenomenon to be
handled both experimentally and theoretically. Sulphuric acid (together with water
vapour) is assumed to be one of the key compounds in atmospheric nucleation, but the
exact nucleation mechanism and the identity of other nucleating compounds, such as
ammonia, amines or some oxygenated organic compounds, are still unknown.
At the start of the research made in this thesis, aerosol instrumentation was limited to
measure only particles larger than 3 nm in diameter. This detection limit prevented
researchers from performing direct measurements of atmospheric nucleation. One aim
of examining the correlation of particle formation with sulphuric acid, the assumed
main nucleating substance, was to obtain indirect information on the processes below
thedetectionlimit: forexample, fromthetimeshiftanalysisthegrowthrateofparticles
< 3 nm could be estimated. The gap between 3 nm and the nucleation size at 1–1.5 nm
was crossed using theoretical methods to account for particle losses in between those
The main part of the research performed in this thesis was devoted to the investigation
of the correlation of new particle formation with the sulphuric acid concentration
(papers I–IV). The number concentration of freshly nucleated particles (3–6 nm in
diameter) as well as the new particle formation rate were observed to correlate with
the sulphuric acid concentration to the power of 1–2. Based on this correlation, new
semi-empirical parameterisations for the atmospheric nucleation rate were developed:
activation nucleation with a linear dependence and kinetic nucleation with a squared
dependence onthesulphuric acidconcentration. Thevalues oftheproportionalitycoefficients
for these nucleation mechanisms, activation coefficient A and kinetic coefficient
K, were determined for three data sets from two different environments in Finland and
Germany. The determination of the empirical A and K coefficients can be considered
as the most valuable result of this thesis. The developed parameterisations, especially
the activation type nucleation, have been used widely by other reseachers in aerosol
dynamical and climate models.
ThelargevariationsinbothAandK (two andthreeordersofmagnitude, respectively),
even at the same measurement site, suggest that there are other important factors
affecting the nucleation process in addition to sulphuric acid. The parameterisations
have been further developed by Paasonen et al. (2010) to include the possible effect
of organic vapours. However, the exact physical and chemical details hidden in the
empirical A and K coefficients remain still unknown. More research, especially insitu
measurements of the chemical composition of nucleated clusters, is needed to
explain the large variation of nucleation coefficients and to develop more accurate
parameterisations for nucleation.
The connection between particle formation and sulphuric acid concentration was further
investigated by means of aerosol dynamical modelling, applying the activation and
kinetic nucleation mechanisms (paper IV). It was found that the correlation exponent
with sulphuric acid concentration was different for the formation rate of 1.5 nm
particles (J 1.5 i.e. the nucleation rate), for the formation rate of 3 nm particles (J 3 ),
and for the number concentration of 3–6 particles (N 3−6 ). When going from J 1.5 to J 3
and N 3−6 , the value of the correlation exponent could increase by 1–3 units, the change
depending on the particle growth rate and especially its profile as a function of particle
size. In order to obtain close to linear dependence for N 3−6 , activation nucleation and
a negligible saturation concentration for the condensable organics were required, i.e.
the growth rate of freshly nucleated particles needed to be high.
Atmospheric new particle formation happens preferably in conditions with low relative
humidity, which has been explained mainly by high condensation and coagulation
sinks due to water uptake by particles at high humidities. This thesis produced a
new possible hypothesis for the effect of relative humidity on new particle formation
(paper III). The particle formation rate seems to be limited by decreased production
of sulphuric acid at high relative humidities, due to decreased solar radiation reaching
the ground at humid conditions (where clouds may be present). However, a clear
causal relationship between the decreased solar radiation and relative humidity could
not be proven, because these variables have opposite diurnal profiles, thereby creating
an apparent anticorrelation between them. Aerosol dynamical modelling revealed that,
in comparison to the reduced sulphuric acid effect, the previously suggested effects of
increased condensation and coagulation sinks have a smaller contribution in inhibiting
nucleation at high humidities.
With regard to research methods, in this thesis the methods for analysing the correlation
of particle formation rate with sulphuric acid were developed (papers I, II and
IV). Additionally, the accuracy of the conventional method to estimate particle formation
rate from the particle size distribution data was evaluated and a new, slightly
improved method for J 3 calculation was proposed (paper V).
The importance of aerosols in the climate system is primarily associated with their
ability to act as cloud condensation nuclei. The potential of boreal forest aerosols to
act as cloud condensation nuclei was studied based on 1 year of CCN concentration
measurements and hygroscopicity measurements at ground level at the SMEAR II station
(paper VI). The CCN concentration was found to have a seasonal variation with
highest concentrations in summertime, when also the particle growth rates caused by
biogenic organic vapours are the highest. New particle formation events were observed
to almost double the CCN concentrations on the day following the event. Estimates for
the critical diameter of cloud droplet activation and for the hygroscopcity parameter κ
were determined. The values corresponded to a mixture of mainly organicaerosol, with
a small fractionof inorganic sulfates, as expected in the boreal forest environment. The
determined κ-values can be applied in modelling the CCN-activation of boreal forest
aerosols in climate models.
By the time this thesis was finalized, insummer-autumn 2013, huge advances inaerosol
measurement technology have been achieved. Several new developed instruments —
such as AIS, NAIS, PHA-CPC, PSM — have gone below the 3 nm limit, and opened
up the world of aerosol science directly down to the nucleation size at 1–2 nm. This
has increased our understanding of the complicated processes related to atmospheric
new particle formation. Mass spectrometric techniques and the particle size magnifier
(PSM) are closing the gap between molecular clusters (1 nm) and aerosol particles
(> 2–3 nm): in laboratory conditions the growth of nucleated clusters can be followed
molecule by molecule (Kirkby et al., 2011; Almeida et al., 2013). Still, many things
remain to be investigated, e.g.: What is the role of other substances than sulphuric
acid (amines, various organic molecules/vapours) in nucleation and early growth of
nucleated clusters? What is the molecular structure of nucleated and pre-nucleation
clusters? In theobserved cluster pool, arethere different kinds of clusters, and which of
them start to grow further? In the atmosphere, the variety of compounds (especially of
Measurement data both from field and laboratory are needed to get real information
on the quantities and processes under study. In atmospheric data — all processes
happening under one common sun — there are many correlations, but fewer, and
often complex causal relationships between the variables. Careful data-analysis and
modelling can give insights on how the measurement data can be interpreted: what is
the importance of a certain possible reason behind an observed phenomenon, and what
can be concluded based on the data.
As an end product, research will provide useful tools, for example in the form of
nucleation rate parameterisations. These can be applied in regional aerosol and global
climate models, for making predictions of the future and suggestions for the actions
needed to prevent climate change or to improve air quality — for the good of society
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